Capacitive energy storage device

ABSTRACT

Capacitive energy storage devices (CESDs) are disclosed, along with methods of making and using the CESDs. A CESD includes an array of electrodes with spaces between the electrodes. A dielectric material occupies spaces between the electrodes; regions of the dielectric material located between adjacent electrodes define capacitive elements. The disclosed CESDs are useful as energy storage devices and/or memory storage devices.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No.15/828,226, filed Nov. 30, 2017, which claims the benefit of U.S.Provisional Application No. 62/429,651, filed Dec. 2, 2016, and U.S.Provisional Application No. 62/458,426, filed Feb. 13, 2017, each ofwhich is incorporated by reference herein in its entirety.

FIELD

This disclosure concerns embodiments of a capacitive energy storagedevice and methods for making and using the device.

BACKGROUND

Use of capacitors as energy storage and/or memory storage devicesentails the storage of electrical energy in the form of charge usingconductive electrodes. As a method of energy storage, electrostaticcapacitors have excelled at the speed with which they can accumulate anddischarge energy. In general the charge and discharge mechanisms fortraditional electrostatic energy storage in a dielectric material is ina time-domain regime of picoseconds to hundreds of microseconds.Utilization of the storage of charge by a capacitive element in computermemory storage is the basis of much of the memory storage for both flashmemory (ROM, Read Only Memory) and DRAM (Dynamic Random Access Memory).

A need exists for capacitive energy storage devices that include aplurality of capacitive elements and have the versatility to be used asenergy storage and/or memory storage devices.

SUMMARY

Embodiments of capacitive energy storage devices (CESDs) are disclosed,along with methods of making and using the CESDs. A CESD includes aplanar array of electrodes with spaces between the electrodes, the arraycomprising n groups of electrodes in one or more planes, where n is aninteger greater than or equal to 2. A dielectric material occupiesspaces between the electrodes and contacts the electrodes, whereinregions of the dielectric material located between adjacent electrodesdefine capacitive elements.

In one embodiment, the CESD is a stacked CESD and the array comprises ngroups of spaced-apart parallel electrodes forming n stacked parallelplanes of parallel electrodes, each electrode having a central axisparallel to the plane in which the electrode is located. The parallelelectrodes in each plane may be rotated from 0-90° relative to theparallel electrodes in each adjacent plane. In any or all of theforegoing embodiments, the CESD may have a quadrilateral configurationdefining four side edges, wherein each electrode has an end protrudingfrom one side edge of the CESD, and the CESD further comprises aconductive material applied to two or more side edges of the CESD and incontact with the ends of electrodes protruding from the side edges towhich the conductive material is applied. In any or all of the foregoingembodiments, the electrodes may comprise wires having sinuous curves orwires including periodic protrusions along a length of the wire.

In an independent embodiment, the array comprises aligned rows ofelectrodes, each row constituting a group of electrodes. In anotherindependent embodiment, the array comprises staggered rows ofelectrodes, each row constituting a group of electrodes. In anindependent embodiment, the array comprises staggered rows of theelectrodes, each row further comprising a row electrical interconnectconnecting a group of alternating electrodes in the row in series, andgroups of staggered electrodes not connected by the row electricalinterconnect are connected in columns by column electricalinterconnects, the column electrical interconnects being offset from thecentral axes of the staggered electrodes, wherein there is a verticalspatial separation at each intersection where a row electricalinterconnect crosses a column electrical interconnect. In anotherindependent embodiment, the array comprises a grid pattern of rows andcolumns of electrodes, wherein each row comprises electrodes of a rowgroup alternating with electrodes of a plurality of column groups; eachrow group further comprises a row electrical interconnect connectingeach electrode of the row group in series; and each column group furthercomprises a column electrical interconnect connecting each electrode ofthe column group in series, wherein there is a vertical spatialseparation at each intersection where a row electrical interconnectcrosses a column electrical interconnect. In any of the foregoingembodiments, the CESD may further include (i) an insulative layerdisposed between the row electrical interconnects and the columnelectrical interconnects such that the row electrical interconnects areabove the insulative layer and the column electrical interconnects arebelow the insulative layer; and (ii) a via defined by the insulativelayer for each electrode of the row group, the via connecting theelectrode to the row electrical interconnect.

In some embodiments, a CESD comprises a unit cell, the unit cellcomprising (i) a plurality of electrodes at least forming a shape of apolygon with an electrode at each vertex of the polygon; (ii) a numberof electrical interconnects equal to a number of electrodes in the unitcell, each electrical interconnect connected to a single electrode inthe unit cell, wherein there is a vertical spatial separation at eachintersection of two or more electrical interconnects; and (iii) adielectric material occupying spaces between the electrodes, whereinregions of the dielectric material located between adjacent electrodesdefine capacitive elements. The unit cell may further include anelectrode at a center of the polygon. In any or all of the foregoingembodiments, the CESD may further include an insulative layer disposedbetween intersecting electrical interconnects, and a via defined by theinsulative layer to connect an electrical interconnect above theinsulative layer to an electrode below the electrical interconnect andinsulative layer. In some embodiments, the CESD comprises an array ofthe unit cells. Collinear electrodes of a corresponding position in twoor more unit cells may be connected in series through an electricalinterconnect.

In any or all of the above embodiments, the electrodes may have acentral axis-to-central axis spacing between adjacent electrodes withina range of 5 nm to 5 mm. In any or all of the above embodiments in whicheach electrode has a central axis Ac perpendicular to the plane, (i)each electrode may have a height along the central axis of from 5 nm to12000 μm; (ii) each electrode in a group of electrodes may havesubstantially the same height along the central axis; (iii) eachelectrode in the array may have substantially the same height along thecentral axis; or (iv) any combination of (i), (ii), and (iii).

In an independent embodiment, a CESD includes two or more electrodesdisposed in a co-spiral arrangement with spaces between the electrodes,wherein the two or more electrodes do not intersect one another; and adielectric material occupying the spaces between the electrodes. Inanother independent embodiment, a CESD includes a first electrode; asecond electrode wrapped in a spiral configuration around the firstelectrode, wherein there is a space between the first electrode and thesecond electrode; a dielectric material occupying the space between thefirst electrode and the second electrode and in contact with the firstelectrode and the second electrode; and optionally a third electrodehaving a tubular configuration surrounding the first and secondelectrodes, wherein there is a space between the third tubular electrodeand the second electrode, the space filled with the dielectric material,wherein regions of the dielectric material located between theelectrodes define capacitive elements. Additional layers of alternatingpolarity can be optionally constructed as described.

In another independent embodiment, a stacked CESD includes a firstelectrode, a second parallel to and spaced apart from the firstelectrode, thereby forming a space between the first and secondelectrodes, and a stacked arrangement of alternating layers of adielectric material and a conductive material disposed parallel to thefirst and second electrodes and occupying the space between the firstand second electrodes. The stacked arrangement includes x layers of adielectric material, wherein (i) x is an integer greater than or equalto two, (ii) a first layer of the dielectric material is in directcontact with the first electrode, and (iii) layer x of the dielectricmaterial is in direct contact with the second electrode; and y layers ofa conductive material, wherein y=x−1 and a layer of the conductivematerial is positioned between each pair of adjacent layers of thedielectric material. In an independent embodiment, the stacked CESD is atubular stacked CESD wherein (i) the first electrode has a cylindricalconfiguration, an inwardly facing surface, an outwardly facing surface,and an outer diameter; (ii) the second electrode has a cylindricalconfiguration, an inwardly facing surface, an outwardly facing surface,and an inner diameter that is greater than the outer diameter of thefirst electrode; and (iii) the stacked arrangement is disposed betweenthe outwardly facing surface of the first electrode and the inwardlyfacing surface of the second electrode in concentric alternating layersof the dielectric material and the conductive material.

A method for making a CESD includes forming an array of electrodes atleast partially embedded within or in contact with a dielectric materialwith spaces between the electrodes, the array of electrodes comprising ngroups of electrodes arranged in one or more planes, where n is aninteger greater than or equal to 2. In one embodiment, the array ofelectrodes is formed and the dielectric material is disposed in thespaces between the electrodes. In an independent embodiment, a layer ofdielectric material is formed, and electrodes are at least partiallyembedded in the dielectric material or placed in contact with thedielectric material to form the array of electrodes. In an independentembodiment, a method for making a CESD includes (a) providing a firstelectrode; (b) forming a stacked arrangement of alternating layers of adielectric material and a conductive material by (i) applying a layer ofa dielectric material to a surface of the first electrode, (ii) applyinga layer of a conductive material onto the layer of the dielectricmaterial, and (iii) applying a subsequent layer of the dielectricmaterial onto the layer of the conductive material; and (c) applying asecond electrode in contact with an outermost layer of the stackedarrangement; the method may further include sequentially repeating steps(ii) and (iii) to provide additional alternating layers of thedielectric material and the conductive material, the additionalalternating layers terminating with a layer of the dielectric materialsuch that the stacked arrangement includes x layers of the dielectricmaterial alternating with y layers of the conductive material, wherein xis an integer greater than or equal to 2 and y=x−1.

Embodiments of the disclosed CESDs are useful as energy storage devicesand/or memory storage devices. In some embodiments, a method of using aCESD includes providing a CESD as disclosed herein and applying avoltage across a capacitive element disposed between two adjacentelectrodes, wherein the capacitive element is a region of the dielectricmaterial located between the adjacent electrodes, thereby charging thecapacitive element to a voltage V1. In some embodiments, the methodfurther includes supplying energy from the CESD to a load by providing acircuit including the CESD and a load connected to the CESD, wherein thecapacitive element is charged to the voltage V1, and applying a reversedpolarization electric potential across the capacitive element for adischarge period of time, wherein the reversed polarization electricpotential is less than the voltage V1 and less than a voltage that wouldbe generated by the capacitive element in a high impedance state,thereby supplying power from the capacitive element to the load.

In some embodiments, the CESD is a memory device, and the capacitiveelement has a logic state determined by the voltage applied across thecapacitive element. In one embodiment, using the memory devicecomprising the CESD includes writing to the memory device by applying avoltage across a capacitive element disposed between an electrode of afirst group of electrodes and an adjacent electrode of a second group ofelectrodes, wherein the capacitive element is a region of the dielectricmaterial located between the electrode of the first group and theadjacent electrode of the second group, thereby charging the capacitiveelement to a voltage V1. The method may further include reading thememory device by connecting one of a first electrical interconnectconnected to the first group of electrodes and a second electricalinterconnect connected to the second group of electrodes to a highimpedance sensor, connecting the other of the first electricalinterconnect and the second electrical interconnect to Vss, and readingthe voltage V1 of the capacitive element with the high impedance sensor.A memory device comprising a CESD may be refreshed by (i) charging acapacitive element in the CESD to a voltage V1, wherein the voltage V1discharges, at least in part, due to leakage over time; (ii)subsequently determining a capacitance C of the capacitive element;(iii) determining, based on the capacitance C, the voltage V1; and (iv)recharging the capacitive element to the voltage V1.

In any or all of the above embodiments, the dielectric material may be afluid having a viscosity greater than or equal to 0.5 cP. In any or allof the above embodiments, the dielectric material may be anelectroentropic dielectric material that has a relative permittivitygreater than 3.9. In any or all of the above embodiments, the conductivematerial may be a carbonaceous material, a metal, a conductive polymer,or a combination thereof.

The foregoing and other objects, features, and advantages of theinvention will become more apparent from the following detaileddescription, which proceeds with reference to the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following drawings, unless otherwise specified, any apparent gapsbetween elements (e.g., between electrodes and dielectric material) areshown for clarity purposes only and are not present in the actualdevice.

FIG. 1 is a cross-sectional side view of a multilayer capacitor.

FIG. 2A is a cross-sectional side view of an exemplary capacitive energystorage device (CESD).

FIG. 2B is a cross-sectional side view of two CESDs according to FIG. 2Aarranged in a stack.

FIG. 3 is a top plan view of a CESD comprising an array of electrodesarranged in an aligned grid pattern, each diagonal row constituting agroup of electrodes.

FIG. 4 is a top plan view of a CESD comprising an array of electrodesarranged in an aligned grid pattern, each row constituting a group ofelectrodes.

FIG. 5 is a top plan view of a CESD comprising an array of electrodesarranged staggered rows, each row constituting a group of electrodes.

FIG. 6 is a top plan view of a CESD comprising an array of electrodesarranged in offset diagonal rows, each row constituting a group ofelectrodes.

FIG. 7 is a top plan view of a CESD comprising an array of electrodesarranged in an aligned grid pattern, each row including electrodesconstituting a row group alternating with electrodes of a plurality ofcolumn groups and each column including electrodes constituting a columngroup alternating with electrodes of a plurality of row groups; eachinterior electrode is surrounded by four capacitive elements.

FIG. 8 is a cross-sectional side view of the CESD of FIG. 7 taken alongline 8-8.

FIG. 9 is a cross-sectional side view of a CESD comprising an array ofelectrodes arranged in an aligned grid pattern, each row includingelectrodes constituting a row group alternating with electrodes of aplurality of column groups and each column including electrodesconstituting a column group alternating with electrodes of a pluralityof row groups; the row groups and column groups are connected byelectrical interconnects positioned at different heights relative to asubstrate or lower surface of the electrodes.

FIG. 10 illustrates activation of a single edge row group and a singleinterior column group of the CESD of FIG. 7, thereby accessing a singlecapacitive element.

FIG. 11 illustrates activation of a single interior row group and asingle interior column group of the CESD of FIG. 7, thereby accessingtwo capacitive elements on opposing sides of a row electrode.

FIG. 12 illustrates activation of a single interior row group and asingle interior column group of the CESD of FIG. 7, thereby accessingtwo capacitive elements on opposing sides of a column electrode.

FIG. 13 is a top plan view of a CESD comprising an array of electrodesarranged in staggered rows, each row including electrodes constituting arow group alternating with electrodes of a plurality of column groups;each interior electrode is surrounded by four capacitive elements.

FIG. 14 illustrates activation of a single interior row group and asingle interior column group of the CESD of FIG. 13, thereby accessingfour capacitive elements.

FIG. 15 is a top plan view of a CESD comprising an array of hexagonalelectrodes arranged in staggered rows, each row constituting a group ofelectrodes.

FIG. 16 is a top plan view of a CESD comprising a plurality ofelectrodes arranged in a polygonal unit cell configuration.

FIG. 17 is a top plan view of a CESD comprising a plurality of thepolygonal unit cells of FIG. 16.

FIG. 18 is a top plan view of a CESD comprising two or more electrodesin a co-spiral arrangement.

FIG. 19 is a simplified schematic diagram of a device comprising a CESD,a switching array, and a controller.

FIG. 20 is a perspective view of an exemplary tubular CESD having afirst electrode and a second electrode in a spiral configuration aroundthe first electrode.

FIG. 21 is a perspective view of an exemplary tubular CESD having afirst electrode, a second electrode in a spiral configuration around thefirst electrode, and a tubular third electrode surrounding the first andsecond electrodes.

FIGS. 22A and 22B are a cross-sectional side view (22A) and aperspective view (22B) of an exemplary stacked CESD.

FIG. 23 is a cross-sectional side view of an exemplary stacked CESDfurther including a sealing material on side edges of the CESD.

FIGS. 24A-24C are a perspective view, a bottom view, and across-sectional side view, respectively, of an exemplary stacked CESDincluding a plurality of layers of parallel electrodes wherein theelectrodes in a given layer have a common polarity, electrodes inadjacent layers have opposite polarities, and electrodes in each layerare oriented at right angles relative to electrodes in the adjacentlayer(s).

FIG. 25 is a perspective view of an exemplary stacked CESD including aplurality of layers of parallel electrodes wherein the electrodes in agiven layer have a common polarity, electrodes in adjacent layers haveopposite polarities, and the parallel electrodes in each layer arerotated such they are not oriented at right angles relative to theparallel electrodes in the adjacent layer(s).

FIGS. 26A-26D are, respectively a perspective view, a bottom view, andtwo cross-sectional side views of an exemplary stacked CESD including aplurality of layers of parallel electrodes wherein the electrodes in agiven layer have alternating polarities, and electrodes in each layerare oriented at right angles relative to electrodes in the adjacentlayer(s). In FIG. 26C, there is a plane/plane offset of the electrodes;in FIG. 26D, the electrodes are vertically aligned.

FIGS. 27A and 27B show two parallel arrangements of twisted wireelectrodes wherein adjacent electrodes have the same polarity (27A) oropposite polarities (27B).

FIGS. 28A and 28B show two antiparallel arrangements of twisted wireelectrodes wherein adjacent electrodes have the same polarity (28A) oropposite polarities (28B).

FIGS. 29A and 29B show two parallel arrangements of wire electrodes,each electrode including periodic protrusions along the length of theelectrode, wherein adjacent electrodes have the same polarity (29A) oropposite polarities (29B).

FIGS. 30A and 30B show two antiparallel arrangements of wire electrodes,each electrode including periodic protrusions along the length of theelectrode, wherein adjacent electrodes have the same polarity (30A) oropposite polarities (30B).

FIG. 31 is a cross-sectional view of an exemplary tubular stacked CESDhaving a cylindrical configuration.

FIG. 32 is a cross-sectional view of the tubular stacked CESD of FIG.31, wherein the tubular stacked CESD further includes an optional outernonconductive coating.

FIG. 33 is as schematic diagram illustrating possible series andparallel connections of capacitive elements in a CESD.

FIG. 34 shows several exemplary combinations of two capacitive elementsin series or parallel.

FIG. 35 is a flow diagram of a generalized method of making a CESD asdisclosed herein.

FIG. 36 is a flow diagram of a generalized method of making a CESDincluding intersecting electrical interconnects.

FIG. 37 is a flow diagram of a generalized method of making a stackedCESD as shown in FIGS. 22A and 22B.

FIG. 38 is a flow diagram of one generalized method for making a stackedCESD as shown in FIGS. 24-26.

FIG. 39 is a flow diagram of another generalized method for making astacked CESD as shown in FIGS. 24-26.

FIG. 40 is a flow diagram of a generalized method of charging a CESD asdisclosed herein.

FIG. 41 is a flow diagram of a generalized method of supplying energyfrom a CESD as disclosed herein to a load.

FIG. 42 is a flow diagram of a generalized method of charging a stackedCESD as disclosed herein.

FIG. 43 is a flow diagram of a generalized method of supplying energyfrom a stacked CESD as disclosed herein to a load.

FIG. 44 is a flow diagram illustrating one method of writing to a memorydevice comprising a CESD as disclosed herein and reading the memorydevice.

FIG. 45 is a flow diagram illustrating one method of determining thecapacitance of a capacitive element in a memory device comprising a CESDand refreshing the CESD.

FIG. 46 is a flow diagram illustrating one method of reading acapacitive element in a memory device in ROM mode, the memory devicecomprising a CESD.

DETAILED DESCRIPTION

Embodiments of capacitive energy storage devices (CESDs) and methods ofmaking and uses using such devices are disclosed. Embodiments of thedisclosed devices include a plurality of electrodes and a plurality ofcapacitive elements. The CESDs can be used as energy storage devicesand/or as ROM and/or RAM memory devices for retention of information indigital format. The CESDs disclosed herein have increased ability tostore charge and also discharge the stored electrical energy to providea greater energy density (energy per unit volume) and specific energy(energy per unit mass) than previously known and manufactured devices.

I. Definitions

The following explanations of terms and abbreviations are provided tobetter describe the present disclosure and to guide those of ordinaryskill in the art in the practice of the present disclosure. As usedherein, “comprising” means “including” and the singular forms “a” or“an” or “the” include plural references unless the context clearlydictates otherwise. The term “or” refers to a single element of statedalternative elements or a combination of two or more elements, unlessthe context clearly indicates otherwise.

Unless explained otherwise, all technical and scientific terms usedherein have the same meaning as commonly understood to one of ordinaryskill in the art to which this disclosure belongs. Although methods andmaterials similar or equivalent to those described herein can be used inthe practice or testing of the present disclosure, suitable methods andmaterials are described below. The materials, methods, and examples areillustrative only and not intended to be limiting. Other features of thedisclosure are apparent from the following detailed description and theclaims.

Unless otherwise indicated, all numbers expressing quantities ofcomponents, voltages, temperatures, times, and so forth, as used in thespecification or claims are to be understood as being modified by theterm “about.” Accordingly, unless otherwise indicated, implicitly orexplicitly, the numerical parameters set forth are approximations thatmay depend on the desired properties sought and/or limits of detectionunder standard test conditions/methods as known to those of ordinaryskill in the art. When directly and explicitly distinguishingembodiments from discussed prior art, the embodiment numbers are notapproximates unless the word “about” is recited.

In order to facilitate review of the various embodiments of thedisclosure, the following explanations of specific terms are provided:

Array: An orderly arrangement, e.g., of rows, columns, or a regularlyrepeating pattern.

Capacitance: The ability of a body to store an electrical charge.Capacitance is defined as

${C = \frac{Q}{V}},$

where Q is charge (coulombs) and V is potential (volts). Capacitance istypically expressed in farads, where 1 F=1 C/V.

Capacitive element: As used herein, the term “capacitive element” refersto a region of a dielectric material located between two adjacentelectrodes that are not serially connected.

CESD: Capacitive energy storage device.

Coplanar: The term “coplanar” is an adjective describing two or moreobjects, each object having at least one surface located on a commongeometric plane. Thus, electrodes that are disposed on a single planarsubstrate or carrier are coplanar. Similarly, electrical interconnectsthat are disposed on a common insulative layer, disposed atop aplurality of coplanar electrodes of substantially the same height,and/or occupy the same geometric plane in space are coplanar.

Co-spiral: As used herein, the term “co-spiral” refers to two or moreintermingled spirals. When referring to a co-spiral of two or moreelectrodes, the electrodes are electrically independent (i.e., theindividual electrodes do not intersect one another). A co-spiralarrangement of electrodes may be formed, for example, by laying twowire- or line-type electrodes side-by-side with a space between the twoelectrodes, and then arranging the two electrodes together into a spiralshape such that the rings of the spiral alternate between the firstelectrode and the second electrode, and such that the electrodes do notintersect one another, e.g., as shown in FIG. 18. The co-spiral isplanar when the electrodes are arranged into a co-spiral on a planarsurface. The term “co-spiral” encompasses spirals having a substantiallycircular elliptical, polygonal, or irregular spiral shape.

Dielectric material: An electrical insulator that can be polarized by anapplied electric field.

Electrical interconnect: An electrically conductive line used to connecta plurality of electrodes in series.

Electrically insulative material or insulator: An insulator is amaterial having internal electric charges that do not flow freely, andtherefore the material conducts little or no electric current.Recognizing that perfect insulators do not exist, as used herein, theterm “electrically insulative material” refers to a material that isprimarily insulative, i.e., a material that has a threshold breakdownfield that exceeds an electric field applied across the material duringnormal use as a capacitor, thus avoiding electrical breakdown duringnormal use.

Electrode: As used herein, the term “electrode” refers to an electricalconductor (e.g., a metal) or to a “composite” electrode comprising anelectrical conductor and a nonconductive material on the surface of theelectrical conductor. Exemplary electrodes include metals, electricallyinsulated metals, carbonized polymers, conductive carbon, andelectrically conductive polymers.

Entropic material: A material in which energy is stored via entropicchanges of the material. In some examples, the entropic changes aredriven by electrical means, and the material is referred to as anElectroentropic™ material. In other examples, the entropic changes aredriven by magnetic fields, and the material is referred to as aMagnetoentropic™ material. Entropic changes include atomic, molecular,secondary, and/or tertiary structure changes, such as intramolecularmovement of polymers and/or intermolecular movement of charged or polarmolecular species within the material. Embodiments of the disclosedentropic materials comprise a plurality of polymeric molecules,particularly polymeric molecules including one or more polar functionalgroups and/or ionizable functional groups.

Graphene: an extremely electrically conductive form of elemental carbonthat is composed of a singe flat sheet of carbon atoms arranged is arepeating hexagonal lattice.(https://www.merriam-webster.com/dictionary/graphene).

Graphitic carbon: Graphitic carbon comprises carbon in the allotropicform of graphite, irrespective of the presence of structural defects andthe percentage of the graphite structure. Graphitic carbon has at leastsome domains exhibiting three-dimensional hexagonal crystallinelong-range order as detected by diffraction methods (IUPAC Compendium ofChemical Terminology, 2nd ed. (the “Gold Book”), compiled by A. D.McNaught and A. Wilkinson, Blackwell Scientific Publications, Oxford(1997). XML on-line corrected version: http://goldbook.iupac.org (2006-)created by M. Nic, et al.; updates compiled by A. Jenkins. ISBN0-9678550-9-8. doi:10.1351/goldbook, updated Feb. 24, 2014, version2.3.3).

Graphitized carbon: As defined by IUPAC, graphitized carbon is agraphitic carbon with more or less perfect three-dimensional hexagonalcrystalline order prepared from nongraphitic carbon by graphitizationheat treatment, i.e., heat treatment at a temperature within a range of2500-3300 K (Ibid.). As used herein, the term partially graphitizedcarbon refers to graphitic carbon with a graphite-type structure contentwithin a range of from 20 to 99% by weight, such as from 50 to 99% orfrom 80-95% by weight.

Insulative or nonconductive layer/coating: As used herein, the terms“insulative layer,” “insulative coating,” “nonconductive layer,” and“nonconductive coating” refer to a layer or coating of a material thatis electrically insulative from an Ohmic conductivity standpoint, i.e.,the material has an Ohmic conductivity less than 1×10⁻¹ S/m (Siemens permeter).

Parylene: Polymerized p-xylylene, also known as a Puralene™ polymer(Carver Scientific, Inc.), or polymerized substituted p-xylylene.Poly(p-xylylene) satisfies the formula:

Permittivity: As used herein, the term “permittivity” refers to theability of a material to become polarized, thereby changing the“dielectric constant” of its volume of space to a higher value than thatof a vacuum. The relative permittivity of a material is a measurement ofits static dielectric constant divided by the dielectric constant of avacuum as shown in Eq. 2.

$\begin{matrix}{e_{r} = \frac{e_{s}}{e_{0}}} & {{Eq}.\mspace{14mu} 2}\end{matrix}$

where: er=relative permittivity, es=measured permittivity, andeo=electrical permittivity of vacuum (8.8542×10⁻¹² F/m). A vacuum has arelative permittivity of 1, whereas water has a relativity permittivityof 80.1 (at 20° C.) and an organic coating typically has a relativepermittivity of 3-8. Generally speaking, the term “high permittivity”refers to a material having a relative permittivity of at least 3.3. Asused herein, the term “high permittivity” also refers to a materialhaving a permittivity enhanced by at least 10% using a permittivityenhancement technique, such as immersion in an electric field.

Perturbing charge: A charge applied to an electroentropic energy device,the charge having a magnitude effective to cause a change in the voltageof the device without changing the capacitance of the device.

Polar: The term “polar” refers to a compound, or a functional groupwithin a compound, in which electrons are not equally shared between theatoms i.e., areas of positive and negative charges are at leastpartially permanently separated.

Polymer/polymeric molecule: A molecule of repeating structural units(e.g., monomers) formed via a chemical reaction, i.e., polymerization. Abiopolymer is a polymer occurring within a living organism, e.g., aprotein, cellulose, or DNA.

RAM: Random-access memory.

ROM: Read-only memory.

Sinuous: Having periodic curves, serpentine.

Unit cell: As used herein, the term “unit cell” refers to a minimumnumber of electrodes to form a CESD. A dielectric material occupiesspaces between the electrodes.

Via: A via (or vertical interconnect access) is electrical connectionthat goes through the plane of a layer. As used herein, a via refers toan electrical connection that extends through an insulative layer toprovide an electrical connection between an electrode and a conductiveline.

Vss: Voltage source supply. As used herein, Vss usually refers to themore negative supply voltage for a circuit including a CESD. In someinstances, Vss is ground. However, Vss is used to indicate a voltagethat is different from the voltage source and can be either higher orlower in voltage than the voltage source. When one electrode (or groupof electrodes in a CESD is connected to a voltage source, anotherelectrode (or group of electrodes) is connected to Vss, where Vss has adifferent voltage than the voltage source, thereby providing a voltagedifference across a capacitive element in the CESD.

II. Capacitive Energy Storage Devices (CESDs)

In some embodiments, a capacitive energy storage device (CESD) comprisesat least two electrodes with a space between the two electrodes, and adielectric material disposed in the space between the two electrodes andin contact with the two electrodes. The CESD may comprise an array ofelectrodes with spaces between the electrodes, the array of electrodescomprising n groups of electrodes in one or more planes, where n is aninteger greater than or equal to 2.

The electrodes may have virtually any geometric cross-sectionalconfiguration, including, but not limited to, a circular cylindricalconfiguration, an elliptic cylindrical configuration, a polygonalcylindrical configuration, a spherical configuration, a hemisphericalconfiguration, or the electrode may have a flat configuration where theelectrode is flat in two dimensions. In certain embodiments as discussedin detail below, the electrodes may comprise wires having sinuous curvesor wires including periodic protrusions along a length of the wire. Inone embodiment, the electrodes have a right circular cylindricalconfiguration. A cylindrical configuration can be used to increaseeffective surface area between electrodes. In an independent embodiment,the electrode has a spherical or hemispherical configuration. In someembodiments, the electrode configuration may affect permittivity of thedielectric. Without wishing to be bound by a particular theory ofoperation, a curved electric field may be able to store more energy thana linear electric field. The electrodes may have a regular (e.g.,smooth) or irregular (e.g., rough) surface. In some embodiments, arandomly irregular or rough electrode surface provides fast charge anddischarge for at least some portion of a charge/discharge cycle. Withoutwishing to be bound to a particular theory of operation, a rough surfacemay provide a faster charge/discharge due to increased surface arearelative to an electrode with a regular, smooth surface. The electrodesare constructed of a conductive material. Suitable conductive materialsinclude, but are not limited to, conductive carbon, a conductive organicmaterial other than carbon, a conductive metal, or a semiconductor. Insome embodiments, the electrodes are anodized (i.e., have a durable,corrosion-resistant, anodic oxide surface film). In other embodiments,the electrodes are coated with an insulative coating such as, forexample, polyp-xylylene).

In some embodiments, the central-to-central axis spacing betweenadjacent electrodes is within a range of 1 nm to 5 mm, such as a spacingfrom 0.03 μm to 1 mm, from 0.5 μm to 100 μm, from 0.1 μm to 50 μm, from1 μm to 500 μm, or from 10 μm to 2000 μm. Thus, a CESD may include from4 to 4×10¹² electrodes/cm², such as from 100 to 1×10⁹ electrodes/cm²,from 1×10⁴ to 1×10⁹ electrodes/cm², or from 2×10⁵ to 5×10⁶electrodes/cm². The electrode spacing may depend, in part, upon theelectric field (E-field) that is desired, the dielectric material used,and/or the presence of an anodized film or insulative coating on theelectrodes. In some embodiments, an applied E-field in the range of from0.0001 V/μm to 1000 V/μm or more, based on an average thickness of thedielectric material, is utilized. In certain embodiments, the appliedE-field is within a range of 0.001 V/μm to 1000 V/μm, 0.001 V/μm to 100V/μm, 100 V/μm to 1000 V/μm, or 1 V/μm to 5 V/μm depending on theintended use of the CESD. When the electrodes include an insulativecoating, very low E-fields due to the blocking effect of the insulativelayer can be used with slightly conductive dielectric materials.Alternatively, transmissive pores in the insulative dielectric can beused to transmit the E-field through the bulk of the insulative coatingto the higher permittivity dielectric. Either larger or smaller spacingof the electrodes (depending on the desired usable voltage of thedevice) is possible when they are anodized or coated with an insulativelayer. Much higher voltages can be realized in such embodiments. In someexamples, voltages in the range of 25 V or greater have been usedwithout an applied insulative coating on the electrodes. Most metalsdevelop a thin non-conductive oxide layer when exposed to atmosphericoxygen. When electrodes have an applied insulative coating, voltages of100 V or more, such as >150 V, >200 V, >250 V, >400 V, or even>650 V maybe applied.

FIG. 1 is a cross-sectional view of a conventional capacitor 10comprising a plurality of electrodes 11, 12 in a parallel configuration.Edge connectors 13, 14 are for external electrical connections. Anonconductive dielectric material 15 is between the electrodes 11, 12.Any apparent gaps between elements of the capacitor are shown forclarity purposes only and are not present in the actual device. Typicalcapacitors made in this manner include multilayer ceramic capacitors(MLCCs), which are used for electronics.

In contrast, some embodiments of the disclosed capacitive energy storagedevices include an array of electrodes in a planar arrangement withspaces between the electrodes and a dielectric material occupying spacesbetween the electrodes. The CESD may be formed on a single planarsurface. This is advantageous for manufacture since the single planefacilitates geometric and mechanical alignment of closely-spacedelectrodes. If the electrodes are not accurately aligned, then theywould contact each other and make a short circuit or cause unwantedinternal discharge of the stored energy. Although two planes ofelectrodes at the micron or nanometer scale can be aligned or registeredaccurately, it is difficult to make large-scale production of suchdevices. The geometric nature of some embodiments of the disclosed CESDshelps alleviate those alignment problems, as only a single planarsubstrate is used during manufacture. Nonetheless, other arrangementswhere electrodes are formed on two or more different planes and thenaligned with the dielectric between the planes is feasible, particularlyin cases where there are fewer electrodes and/or greater spacing betweenelectrodes are also within the scope of this disclosure. In suchembodiments, the edge connectors also may be on two or more differentplanes.

Exemplary CESDs are illustrated in the figures. It is to be understoodthat in CESDs including more than two electrodes, the number ofelectrodes depicted in the figures is representative only and does notindicate a minimum or maximum number of electrodes in the CESD. Inseveral figures, one or more “unit cells” are indicated with dottedlines. The unit cell is the smallest configuration for that CESD.

FIG. 2A is a cross-sectional side view of an exemplary CESD 100comprising a plurality of electrodes 110, 120 in a substantially planararray (i.e., an ordered arrangement) with spaces between the electrodes,each electrode having a central axis Ac perpendicular to the plane. Edgeconnectors 130, 140 are for external electrical connections to theelectrodes. A dielectric material 150 occupies the spaces between theelectrodes 110, 120 and contacts the electrodes. The electrodes 110, 120are at least partially embedded in or in contact with the dielectricmaterial 150. The electrodes 110, 120 may be completely embedded in thedielectric material 150. Regions of the dielectric material locatedbetween adjacent electrodes define capacitive elements. Any apparentgaps between elements of the CESD are shown for clarity purposes onlyand are not present in the actual device.

The plurality of electrodes may be disposed on a substrate, oroptionally removable carrier layer, 160 (the CESD may be formed on acarrier layer, which is subsequently removed). The CESD 100 furthercomprises a plurality of electrical interconnects (not shown in FIG. 2)each electrical interconnect connecting two or more electrodes inseries. Electrodes connected by a single electrical interconnectconstitute a group of electrodes. In some embodiments, the CESD furtherincludes an upper sealing layer or additional dielectric, 170. The CESDincludes at least two groups of electrodes, but may include hundreds oreven thousands of individual electrodes or groups of electrodes. TheCESD includes a number of electrical interconnects equal to the numberof groups of electrodes. Thus, the CESD also includes at least twoelectrical interconnects, but may include hundreds or even thousands ofelectrical interconnects.

As shown in FIG. 2B, two or more CESDs 100 may be vertically stacked toform a CESD stack. A CESD stack may include tens, hundreds, or eventhousands of layered CESDs. Some embodiments of the disclosed CESDs havea thickness ranging from 0.005 μm to 150 μm. Thus, a CESD stack having athickness of just 1 cm can include from 2-2,000,000 layers, such as from50-1,000,000 layers, 50-100,000 layers, 500-50,000 layers, 1,000-10,000layers, or 1,000-7,000 layers. In one embodiment, each CESD in the stackincludes a substrate 160, such as a non-conductive substrate. In anindependent embodiment, a sealing layer 170 is disposed between eachpair of adjacent CESDs in a stack; advantageously the sealing layer isan insulative layer, such as polyp-xylylene) or additional dielectricmaterial. Although FIG. 2B shows a particular number of electrodes, itis understood that a CESD may have more or fewer electrodes than shown.Dotted lines show an interior unit cell 101 a, and an edge or exteriorunit cell 101 b, each including two electrodes and dielectric materialbetween the electrodes. Any apparent gaps between elements of the CESDare shown for clarity purposes only and are not present in the actualdevice.

The electrodes 110, 120 may have any desired height along the centralaxis. In some embodiments, the electrodes have a height of from 1 nm to12000 μm, such as a height of 5 nm to 12000 μm, 0.01 μm to 10 mm, 0.01μm to 1 mm, 0.03 μm to 1 mm, 0.03 μm to 100 μm, a 0.03 μm to 10 μm, 0.5μm to 10 μm, or 1 μm to 10 μm. In certain embodiments, each electrode ina group of electrodes has substantially the same height (i.e., theheight of each individual electrode in the group varies by less than 5%from an average height of the electrodes in the group). In any of theforegoing embodiments, each electrode in the array of electrodes mayhave substantially the same height. The dielectric material occupyingthe spaces between the electrodes may have an average thickness rangingfrom 10% to 5000% of the average height of the electrodes, such as anaverage thickness ranging from 10-1500%, from 90-1500%, from 10-500%, orfrom 90-500% of the average electrode height. In some embodiments, theaverage dielectric material thickness is substantially the same (i.e.,varies by less than 5%) as the average electrode height.

As discussed above, the electrode spacing may depend, in part, upon theelectric field (E-field) that is desired, the dielectric material used,and/or the presence of an anodized film or insulative coating on theelectrodes. In general, the E-field will be perpendicular to the centralaxes of the electrodes. Thus, if the electrodes are disposed on asubstrate such that the central axes are perpendicular to the substrate,the E-field will be substantially parallel to the substrate. In otherembodiments utilizing rounded or curved surfaces, the E-field may have asubstantially curved shape in perspective to a perpendicular point onthe surface of the substrate or electrode.

Exemplary substrates are nonconductive or comprise a nonconductive orinsulative layer (e.g., a polyp-xylylene) layer) in contact with theelectrodes. In some embodiments, the substrate is constructed of amaterial other than silicon, such as a nonconductive polymer. In someembodiments, the substrate 160 is a removable carrier and is removedafter the CESD is assembled. In some examples, a removable carriercomprises a water-soluble polymer.

The electrical interconnects are conductive lines connecting two or moreelectrodes in series. The electrical interconnects may be constructed ofa conductive material, such as conductive carbon, a conductive organicmaterial other than carbon, or a conductive metal. In some embodiments,the electrical interconnects are metal wires. Electrical connections tothe electrodes may be direct or indirect. Direct connections can be madeby methods well known to those who work in the fields ofmicroelectronics and lithography. Connections can be made, for example,using standard wire-bonding machinery or conductive adhesives.

There are many possible electrode arrangements in a CESD, a few of whichare described herein. The same numbering for individual components willbe adhered to throughout FIGS. 3-14. In one exemplary embodiment shownin FIG. 3, a CESD 300 comprises an array of electrodes 110, 120 arrangedin an aligned grid pattern such that the central axis Ac (*) of eachelectrode is aligned with the central axes of immediately adjacentelectrodes of neighboring rows and columns. Each diagonal row (as viewedfrom the top) constitutes a group of electrodes. As indicated by thedotted lines, four electrodes form a unit cell, e.g., cells 301 a, 301b, 301 c. When viewed in diagonal rows, it is seen that the central axesof the electrodes in any row are staggered, or offset, from the centralaxes of electrodes in immediately adjacent diagonal rows. All electrodesin each group of electrodes are connected in series by an electricalinterconnect 115, 125. For example, labeled electrical interconnect 115of FIG. 3 connects two electrodes 110 in series, and labeled electricalinterconnect 125 connects three electrodes 120 in series. Eachelectrical interconnect has a terminal end coupled to an edge connector130, 140, which is used to form external electrical connections for eachgroup of electrodes. Each edge connector 130, 140 may be connected, forexample, to a switch (not shown). The other terminal end of theelectrical interconnect is connected to the electrode in the group thatis farthest from the electrical interconnect. A dielectric material 150occupies spaces between the electrodes 110, 120, and the electrodes areat least partially embedded in or in contact with the dielectricmaterial. Regions of the dielectric material between adjacent electrodesof different groups (electrodes of neighboring diagonal rows) definecapacitive elements 155. In the arrangement of FIG. 3, each interiorelectrode (i.e., an electrode that is not on the edge of the array) issurrounded by four electrodes from other groups. Hence, there are fourcapacitive elements 155 around each interior electrode. Advantageously,the diagonal arrangement of electrode groups allows the edge connectors130, 140 to be spaced apart at twice the distance (center-to-center) ofthe electrodes 110, 120. Capacitive elements are not formed between twoelectrodes serially connected in a single row. Activating a row ofelectrodes 110 and an adjacent row of electrodes 120 will address allcapacitive elements 155 located between the two activated rows.“Activating” means to (i) apply a voltage to an edge connector, (ii)connect the edge connector to Vss (e.g., ground), or (iii) connect theedge connector to a load. For example, a voltage may be applied to anedge connector 130 while an edge connector 140 of an adjacent row isconnected to Vss, where Vss is different than the applied voltage,thereby creating a voltage difference across capacitive elements 155located between electrodes 110 and 120 of the adjacent rows. It shouldbe noted that there are two connections to a capacitor. Since the energystorage is related only to the amount of charge and capacitance of thedevice and therefore the voltage difference between the two connections.We will simplify the discussion by assuming the voltage of oneconnection to the capacitor is ground potential. We will therefore needto only discuss the voltage of the other connection to the capacitivedevices. However, the descriptions and utility of the devices need notbe limited to only ground potentials as is commonly known to thoseversed in electrical circuits.

In the arrangement of FIG. 4, a CESD 400 comprises an array ofelectrodes 110, 120 arranged in an aligned grid pattern such that thecentral axis (*) of each electrode is aligned with the central axes ofimmediately adjacent electrodes of neighboring rows. Each rowconstitutes a group of electrodes. As indicated by the dotted lines,four electrodes form a unit cell 401. The arrangement of aligned rowsprovides two capacitive elements 155 on opposing sides of each interiorelectrode (e.g., electrode 120 a). A single capacitive element 155 isadjacent each edge electrode. Activating a row of electrodes 110 and anadjacent row of electrodes 120 will address all capacitive elements 155located between the two activated rows.

FIG. 5 illustrates a CESD 500 in which the electrodes 110, 120 arearranged in an array of staggered rows, such that the central axis (*)of each electrode in a row is not aligned with the central axes ofelectrodes in neighboring rows. Each row constitutes a group ofelectrodes. As indicated by the dotted lines, four electrodes form aunit cell 501. Each interior electrode (e.g., electrode 120 a) isadjacent to two electrodes in each of the neighboring rows. Thearrangement of aligned rows provides four capacitive elements 155 aroundeach interior electrode, with two capacitive elements on each of theopposing sides of the electrode. Activating a row of electrodes 110 andan adjacent row of electrodes 120 will address all capacitive elements155 located between the two activated rows.

In the embodiment of FIG. 6, a CESD 600 comprises electrodes 110, 120arranged in an array of offset diagonal rows, each row constituting agroup of electrodes. As indicated by the dotted lines, four electrodesform a unit cell 601. Each interior electrode (e.g., electrode 120 a) isadjacent to two electrodes in each of the neighboring diagonal rows. Thearrangement provides four capacitive elements 155 around each interiorelectrode. Activating a row of electrodes 110 and an adjacent row ofelectrodes 120 will address all capacitive elements 155 located betweenthe two activated rows.

FIG. 7 shows a CESD 700 comprising an array of electrodes 110, 120arranged in a grid pattern of aligned rows and columns. Each rowcomprises electrodes of a row group, i.e., electrodes 110, alternatingwith electrodes of a plurality of column groups. Each column constituteselectrodes of a column group, i.e., electrodes 120 alternating withelectrodes of a plurality of row groups. As indicated by the dottedlines, four electrodes form a unit cell 701. Electrodes of each rowgroup are connected in series with a row electrical interconnect 115.Electrodes 120 of each column group are connected in series with acolumn electrical interconnect 125. The arrangement provides fourcapacitive elements 155 around each interior electrode. In theembodiment shown in FIG. 7, the electrical interconnect 125 is offsetfrom the central axes Ac of electrodes 120 and has a branchedconfiguration to connect to each electrode 120. Since the electricalinterconnects 115, 125 cross one another, the interconnects are locatedin different planes in 3-dimensional space. The electrical interconnectsare configured such that vertical spatial separation is present at eachintersection where a row electrical interconnect 115 crosses a columnelectrical interconnect 125. In some embodiments, such as CESD 800 asshown in FIG. 8, an insulative layer 190 is disposed between theelectrical interconnects 115 and 125 such that electrical interconnects115 are above the insulative layer and electrical interconnects 125 arebelow the insulative layer. Electrodes 110 may be connected to theelectrical interconnect 115 by a via 180 extending through theinsulative layer. Alternatively, the insulative layer may be selectivelyremoved above electrodes 110 so that the electrodes can be connected tothe electrical interconnect. A unit cell 801 is indicated by the dottedlines. In an independent embodiment, electrodes 110 have a heightsufficient to extend through the insulative layer (not shown). Inanother independent embodiment, CESD 900 as shown in FIG. 9, the rowelectrical interconnect 115 contacts electrodes 110 at a height h₁ abovea lower surface of each electrode 110. The branched column electricalinterconnect 125 contacts electrodes 120 at a height h₂ above a lowersurface of each electrode 120, where h₁≠h₂. In any of the foregoingembodiments, a sealing layer 170 may be disposed above the uppermostelectrical interconnect.

Advantageously, the configuration shown in FIGS. 7-9 allows addressingof capacitive elements adjacent to a single electrode. This featureprovides tremendous versatility and capacity for energy and/or datastorage. With reference to CESD 1000 of FIG. 10, a single edge row ofelectrodes 110 and a single interior column of electrodes 120 areactivated, e.g., by applying a voltage to edge connector 130 a whileconnecting edge connector 140 g to Vss (e.g., ground). Although allelectrodes connected to the edge connectors 130 a and 140 g areactivated, only a single capacitive element 155 between an activatededge electrode and an activated interior electrode is addressed. Allother regions of the dielectric material 150 are substantiallyunaffected.

FIG. 11 shows a CESD 1100 with activation of an interior row ofelectrodes 110 and an interior column of electrodes 120, e.g., byapplying a voltage to edge connector 130 b while connecting edgeconnector 140 f to Vss. Two capacitive elements 155 located on opposingsides of an activated interior electrode 110 between two activatedelectrodes 120 are addressed. Selection of a different column edgeconnector, e.g., edge connector 140 g (as illustrated with the CESD 1200of FIG. 12), addresses two capacitive elements 155 on opposing sides ofan activated interior electrode 120 between two activated electrodes110. Thus, it can be seen that the capacitive elements adjacent to anysingle electrode can be addressed as desired by activation of one rowand one column of electrodes.

In the arrangement of FIG. 13, a CESD 1300 comprises an array ofelectrodes 110, 120 arranged in a grid pattern of staggered rows suchthat the central axis of each electrode in a row is not aligned with thecentral axes of electrodes in adjacent rows. Each row compriseselectrodes of a row group, i.e., electrodes 110, alternating withelectrodes of a plurality of column groups. As indicated by the dottedlines, four electrodes form a unit cell 1301. Electrodes 110 of each rowgroup are connected in series with a row electrical interconnect 115.Staggered electrodes 120 in a column are connected in series with acolumn electrical interconnect 125. A vertical spatial separation ispresent at each intersection where a row electrical interconnect 115crosses a column electrical interconnect 125. In some embodiments, aninsulative layer (e.g., insulative layer 190 as shown in FIG. 8) isdisposed between the electrical interconnects 115 and 125 such thatelectrical interconnects 115 are above the insulative layer andelectrical interconnects 125 are below the insulative layer. Electrodes110 may be connected to the electrical interconnect 115 by a via 180extending through the insulative layer. The arrangement provides fourcapacitive elements 155 around each interior electrode.

FIG. 14 shows activation of an interior row of electrodes 110 and aninterior column of electrodes 120 in the CESD 1300 of FIG. 13, e.g., byapplying a voltage to edge connector 130 b while connecting edgeconnector 140 d to Vss. The staggered arrangement of electrodesaddresses four capacitive elements 155 by activation of the interior rowand interior column.

Although electrodes 110, 120 are depicted as having a circularcross-section in FIGS. 3-14, the electrodes may have virtually anygeometric configuration as previously discussed. FIG. 15 illustrates aCESD 1500 comprising an array of staggered rows of electrodes 110, 120having a hexagonal cross-section. As indicated by the dotted lines, twoelectrodes form a unit cell 1501. The staggered rows and hexagonalconfiguration provide four capacitive elements 155 adjacent to eachinterior electrode.

In some embodiments, a CESD comprises one or more polygonal unit cellsof electrodes, each polygonal unit cell having five or more sides. Anexemplary polygonal unit cell 1600 is shown in FIG. 16. FIG. 17illustrates a CESD 1700 comprising an array of polygonal unit cells1600. In some embodiments, the array is a planar array of polygonal unitcells 1600. Each polygonal unit cell 1600 comprises a plurality ofelectrodes at least forming the shape of a polygon with an electrode ateach vertex of the polygon. In the exemplary polygonal unit cell of FIG.16, six electrodes (electrodes numbered 2-7) are arranged at thevertices of a hexagon. A person of ordinary skill in the art understandsthat other geometric arrangements are possible. For example, fiveelectrodes may be arranged at the vertices of a pentagon, eightelectrodes may be arranged at the vertices of an octagon, and so on. Insome embodiments, an additional electrode (electrode numbered 1) ispositioned at or near the center of the polygon. The polygonal unit cell1600 comprises a number of electrical interconnects (e.g., interconnects105, 115, 116, 125, 126, 135, 136) equal to the number of electrodes inthe unit cell, each electrical interconnect connected to a singleelectrode in the polygonal unit cell. A dielectric material 150 occupiesspaces between the electrodes, wherein regions of the dielectricmaterial located between adjacent electrodes define capacitive elements155. There is a vertical spatial separation at each intersection of twoor more electrical interconnects. For example, with reference to FIG.16, there is a vertical spatial separation at the intersection ofelectrical interconnects 115, 125. Electrical interconnects that do notintersect each other, however, may occupy the same plane. Thus,electrical interconnects 115, 116 may occupy the same plane, whereaselectrical interconnects 125, 126 occupy another plane verticallyseparated from the electrical interconnects 115, 116. The polygonal unitcell may include insulative layers separating intersecting electricalinterconnects with vias through the insulative layers to connectelectrodes to the corresponding electrical interconnects, similar to theembodiment shown in FIG. 8. Optionally, a sealing layer (not shown) maybe disposed above the uppermost electrical interconnect. In theexemplary unit cell of FIG. 16, the electrical interconnects 105,115/116, 125/126, and 135/136 are disposed in four planes, respectively,and insulative layers may be disposed between the planes. It should benoted that although electrical interconnect 105 is aligned with theelectrodes numbered 1, 2, and 5 in FIG. 16, the electrical interconnect105 is connected only to the electrode numbered 1 at the polygon center,and is separated from the electrodes numbered 2 and 5 (e.g., by aninsulative layer). The electrical interconnects may be connected (e.g.,through edge connectors (not shown)) to external logic circuitry withswitches so that the electrical interconnects can be selectivelyactivated as desired, thereby addressing one or more capacitive elementsin the array.

With further reference to FIG. 17, polygonal unit cells 1600 arearranged such that electrodes in the same position of a plurality ofpolygonal unit cells form a line. For example, the polygonal unit cellsmay be arranged in diagonal rows such that the electrodes at the 12o'clock position (e.g., electrode 110) of two or more polygonal unitcells form a line. As viewed in columns, a center of one hexagonal unitcell is aligned with an edge of a polygonal unit cell in each of theadjacent rows. The collinear electrodes constitute a group of electrodesand are connected with a single electrical interconnect, e.g.,electrical interconnect 115. Each capacitive element 155 is addressedindividually by activating electrodes on opposing sides of thecapacitive element. Each polygonal unit cell in the embodiment of FIG.17 includes 7 electrodes and 21 capacitive elements (12 directly in thepolygonal unit cell and 18 shared with adjacent cells), providing threecapacitive elements per electrodes, each of which can be uniquelyaddressed. A person of ordinary skill in the art will understand thatFIG. 17 shows just one exemplary embodiment of a CESD comprising aplurality of polygonal unit cells, and other polygonal unit cellgeometries and arrangements are encompassed by this disclosure.

The polygonal unit cell arrangement exemplified in FIGS. 16 and 17provides the CESD with tremendous density and capacity. In a case havingan electrode center-to-center spacing of 1 μm, there are threecapacitive elements per micron. Assuming an electrode height of 1 μm,the unit cell arrangement provides a stack density of 10⁹ electrodes/mm³or 10¹² electrodes/cm³, a capacitive element density of 3×10¹²elements/cm³, and 3000 Gb/cm³ or 375 GB/cm³, with each capacitiveelement being one bit (2 logical states).

Advantageously, a CESD comprising an electroentropic dielectric materialgenerates little or no heat during operation, thereby allowing formationand use of large CESD stacks, including stacks having hundreds orthousands of layers, each layer having hundreds or thousands ofelectrodes and capacitive elements. In some embodiments, no heat isdetected during use of the stacked CESD, particularly when the appliedvoltage is no more than 20 V. In some embodiments, the applied voltageis greater than 0 V and <100 V, <75 V, <50 V, <20 V, <10V, or <5V, suchas a voltage from 0.025-20 V, 0.1-10 V, 0.5-5 V, or 0.7-5 V. Incontrast, a conventional stacked capacitor typically is limited to nomore than seven layers of dielectric material, such as SiO₂, beforeheating due to the leakage current becomes excessive.

Table 1 provides exemplary dimensions and properties for several cells,including a “nominal” cell having linear dimensions of 1 μm, a largerelectromagnetic pulse (EMP)-resistant cell, a large “energy collectorand memory cell,” a cell with maximum memory density, and a very largecell useful, for example, energy storage. For robustness, theEMP-resistant cell is assumed to have only 2 logic levels per cell. InTable 1, the term “cell” refers to the area of a single electrode withits associated capacitive elements; a “layer” is a horizontal plane ofcapacitive devices; layers may be stacked in the third dimension; a“unit cell” is the repeating unit for the capacitive array. In theexemplary configurations of Table 1, the unit cell is a hexagonal unitcell with an electrode in the center (e.g., as shown in FIG. 16).

TABLE 1 Energy Maximum EMP- Collector Memory Nominal Resistant andMemory Density Large Cell ¹Linear dimension of cell 1 2.5 20 0.029 100(μm) ²Cell area (μm²) 0.835 5.22 334  7.02 × 10⁻⁴ 8350 ³Electrode 1 2.55 0.029 100 height/dielectric thickness (μm) Spacing between 1 2.5 50.029 100 electrodes (μm) ⁴Optional Insulation layer 0.2 2 1 0.2 5thickness (μm) ⁵Electrical interconnect 0.05 0.05 0.05 0.05 0.05thickness (μm) ⁶Number of additional 2 2 2 2 2 electrical interconnectlayers ⁷Number of additional 1 1 1 1 1 insulative layers Vertical cellthickness 1.5 6.6 7.1 0.529 110.1 with insulation (μm) Number of layersper cm 6667 1515 1408 18904 91 Unit volume (μm³) 1.25 34.4 2370  3.71 ×10⁻⁴ 9.19 × 10⁵ Cells per layer per cm² 1.20 × 10⁸ 1.92 × 10⁷ 2.99 × 10⁵ 1.42 × 10¹¹ 1.20 × 10⁴ Number of cells in 1 cm³  7.98 × 10¹¹  2.90 ×10¹⁰ 4.21 × 10⁸  2.69 × 10¹⁸ 1.09 × 10⁶ Logic levels per cell 8 2 4096 216 ⁸Logic levels per cell as 3 1 12 1 4 binary word (2^(n)) ⁹Number ofcapacitive 3 3 3 3 3 elements per cell Bits per cm³ (Mb) 7.18 × 10⁶ 8.71× 10⁴ 1.52 × 10⁴ 8.07 × 10⁹ 13.1 Bytes per cm³ (MB) 8.98 × 10⁵ 1.09 ×10⁴ 1.90 × 10³ 1.01 × 10⁹ 1.63 Bytes per cm³ (GB) 898 1 2   1 × 10⁶ 0Bytes per cm³ (TB) 0.90 0.01 0   1 × 10³ 0 ¹Electrode spacings areassumed to be equal in both the X and Y dimensions. ²The cell area iscalculated as 6 * (1.5 * spacing)² * sqrt(3)/4/7, where the area of thehexagon is 6 * (l)² * sqrt(3)/4/7, i.e., the unit cell area divided bythe number of electrodes (7), where l is 1.5 * (electrode spacing). ³Theelectrode height and dielectric thickness are assumed to be the same.⁴The base layer of the cell (the insulative layer or substrate on whichthe electrodes are mounted) is assumed to be the same thickness as theinsulation layers between each plane. The dielectric material, or nomaterial at all, may be the only separation material between the planesof the layers. Thus, the insulation layer is completely optional. Forexample, if the bottoms of the conductive traces were anodized, then theseparation of layers could be essentially zero. ⁵Additional electricalinterconnects take up additional thickness on the insulative layers.⁶The first layer of electrical interconnects in direct contact with theelectrodes is not counted. ⁷An even number of electrode layers requires((n/2) − 1) additional insulative layers; an odd number of electrodelayers requires ((n − 1)/2) − 1) additional insulative layers. ⁸Thenumber of logic levels per cell is greatly increased due to the lack ofleakage in the capacitive elements. Four logic levels is equivalent to a2-bit binary logic level device; thus 16 logic levels per cell gives thecell the same number of unique logic outputs as a 4-bit binary logicunit. ⁹The number of capacitive units per cell varies based upon theelectrodes' configurations and interconnections. For a hexagonal unitcell with a center electrode, there are three capacitive elements percell.

Thus, in some embodiments, a CESD 1700 according to FIG. 17 has a cell(electrode and surrounding area) density of from 1×10⁶ to 2.7×10¹⁸cells/cm³, thereby providing the CESD with a memory density of from 1.5to 1×10⁹ MB/cm³. In some embodiments, the CESD has a cell density from4×10⁸ to 2.7×10¹⁸ cells/cm³, from 4×10⁸ to 3×10¹⁶ cells/cm³, or from4×10⁸ to 8×10¹¹ cells/cm³, providing a memory density of from 1 to1,000,000 GB/cm³, from 1-10,000 GB/cm³, or from 1-1,000 GB/cm³.

In another embodiment, as shown in FIG. 18, a CESD 1800 comprises two ormore electrodes 1810, 1820 disposed in a co-spiral arrangement withspaces between the electrodes. Advantageously, the co-spiral arrangementis a planar co-spiral arrangement wherein the electrodes are arranged ona planar substrate. The electrodes do not intersect one another. Each360° loop of the electrodes 1810, 1820 may be considered as a unit cell.An edge connector 1830, 1840 is connected to each electrode 1810, 1820.A dielectric material 1850 occupies the spaces between the electrodes1810, 1820. In some embodiments, the electrodes 1810, 1820 anddielectric material 1850 are disposed on a substrate (not shown), suchas a planar non-conductive substrate. In some embodiments, theelectrodes 1810, 1820 are spaced equidistant from one another throughoutthe spiral arrangement. Although the exemplary arrangement of FIG. 18shows a substantially circular spiral, the electrodes 1810, 1820 may bearranged in any co-spiral shape including, but not limited to, anelliptical, polygonal, or irregular co-spiral, as desired to occupy anavailable space in a device, for example, an integrated circuit. In someembodiments, the electrodes 1810, 1820 have a circular cross-section tomaximize effective surface area.

A device 1900 comprising a CESD may include a CESD 1910, which may beany of the CESDs as disclosed herein, a switching array 1920, and acontroller 1930 including a logic circuit for controlling the switchingarray 1920 as shown in FIG. 19. The switching array 1920 is operable toactivate groups of electrodes in the CESD 1900, thereby addressing oneor more capacitive elements in the CESD, e.g., as described with respectto FIGS. 3-17.

FIG. 20 shows a tubular CESD 2000. The tubular CESD 2000, as illustratedin FIG. 20, comprises a first electrode 2010 and a second electrode2020. Optionally, the first electrode 2010 may have an insulativecoating on its outer surface. As shown, the first electrode 2010 has aright cylindrical configuration. However, the first electrode 2010 mayhave other configurations, such as a polygonal cylinder, an ellipticalcylinder, etc. The second electrode 2020 has a spiral configuration andis wrapped around the first electrode 2010. The second electrode 2020 isadjacent to, but is not in direct contact with, the first electrode2010. The first and second electrodes 2010, 2020 have oppositepolarities during use. A dielectric material (not shown for the sake ofclarity) fills spaces between electrodes 2010, 2020. In someembodiments, the spaces between electrodes 2010, 2020 are created byutilizing a coated wire as the second electrode 2020 and subsequentlyremoving the coating by any suitable means (e.g., a laser or chemicaldissolution) before filling the spaces with the dielectric material.

FIG. 21 shows another embodiment of a tubular CESD 2100. The tubularstacked CESD 2100, as illustrated in FIG. 21, comprises a firstelectrode 2010, a second electrode 2020, and a third electrode 2030. Thefirst electrode 2010 and second electrode 2020 are as described above.The third electrode 2030 has a tubular configuration and encircles orsurrounds the first and second electrodes 2010, 2020 without being indirect contact with second electrode 2020 or first electrode 2010. Thethird electrode 2030 is illustrated as being translucent in FIG. 21simply for the sake of clarity so that the arrangement of electrodes2010 and 2020 can be seen to extend throughout the interior spacedefined by the third electrode 2030. In an actual CESD 2100, the thirdelectrode 2030 is not translucent. The third electrode 4030 has the samepolarity as the first electrode 2010 and has a polarity opposite that ofthe second electrode 2020 during use. A dielectric material (not shownfor the sake of clarity) fills spaces between electrodes 2010, 2020,2030. The first electrode 2010, spiral second electrode 2020, andtubular third electrode 2030 each have a central axis AC, wherein thecentral axes are coaxial. Optionally, the tubular stacked CESD furthercomprises an outer nonconductive sealing material applied to outersurfaces of the third electrode 2030. The outer nonconductive sealingmaterial may electrically isolate the tubular stacked CESD, provideresistance to fluid flow when using a fluid dielectric material, and/orprovide additional mechanical strength to the tubular stacked CESD.Suitable nonconductive sealing materials include, but are not limitedto, polymerized p-xylylene (e.g., Puralene™ polymer), a copolymercomprising p-xylylene and a co-monomer, polyethylene terephthalate,shellac, polyurethane, or cross-linked polyurethane.

It is clear to those versed in multiconductor cable manufacture that theelectrodes illustrated by FIG. 21 can be intertwined around each other.In other words the center electrode could be formed in a spiral manneras to be in close proximity to the outer spiral electrode withouttouching. In the course of winding such a device similar to FIG. 21,such geometrical bending and winding is common. In a similar mannermultiple conductors (electrodes of both polarities) can be woundtogether to make a single bundle (not shown).

Further layers can be added to CESD 2100 by including additionalalternating spiral and tubular electrodes. For instance, another, largerspiral electrode 2020 may be wrapped around the third electrode 2030without being in direct contact with third electrode 2030, and another,larger tubular electrode 2030 may surround the inner layers. All spacesbetween the electrodes are filled with a dielectric material. The numberof layers is only limited by manufacturing and size constraints. Thefirst electrode 2010 and third electrodes 2030 may be connected inparallel using a first electrical interconnect (not shown), and thesecond electrodes 2020 may be connected in parallel using a secondelectrical interconnect (not shown). During use, two or more CESDs 2100can be connected in parallel using electrical interconnects (not shown).

In some embodiments, as shown in FIGS. 22A and 22B, a stacked CESD 2200includes a first electrode 2210, a second electrode 2220 parallel to andspaced apart from the first electrode, thereby forming a space betweenthe first and second electrodes, and a stacked arrangement 2230 ofalternating layers of a dielectric material 2240 and a conductivematerial 2250 disposed parallel to the first and second electrodes andoccupying the space between the first and second electrodes. Connectors2215 and 2225 are for external electrical connections. Apparent gapsbetween elements of the stacked CESD 2200 in FIG. 22A are shown forclarity purposes only and are not present in the actual device. Withreference to FIG. 22A, the stacked arrangement 2230 comprises x layersof a dielectric material, wherein (i) x is an integer greater than orequal to two, (ii) a first layer of the dielectric material 2240 a is indirect contact with the first electrode 2210, and (iii) layer x of thedielectric material 2240 x is in direct contact with the secondelectrode 2220. The stacked arrangement further comprises y layers of aconductive material, wherein y=x−1 and a layer of the conductivematerial is positioned between each pair of adjacent layers of thedielectric material. There is also direct contact between adjacentlayers of dielectric material 2240 and conductive material 2250.

The stacked arrangement 2230 provides a CESD wherein the multiple layersof dielectric material and conductive material are stacked in series.Advantageously, the stacked CESD 2200 requires no internal electricalconnections, other than direct contact, between the stacked alternatinglayers of dielectric material and conductive material. FIG. 22A shows aslight gap between layers such as 2240 and 2250; the gap is shown onlyfor clarity in the drawing. The materials are in direct contact witheach other.

Embodiments of the stacked CESD 2200 include x layers of the dielectricmaterial 2240, wherein x is an integer greater than or equal to two, andy layers of the conductive material 2250, wherein y=x−1. From atheoretical standpoint, the number of layers is essentially unlimited.However, the number of layers may be practically limited bymanufacturing constraints (e.g., difficulty in forming many layershaving a reproducible thickness). In some embodiments, x is an integerfrom 2-5000, 2-1000, 2-500 2-100, 2-50, 2-25, 2-10, or 2-5. For example,x may be 2, 3, 4, 5, 6, 7, 8, 9, or 10. In such arrangements, y is 1, 2,3, 4, 5, 6, 7, 8, or 9, respectively. In the nonlimiting exemplarystacked CESD of FIG. 22A, x is 5 and y is 4.

Each conductive material layer may have a thickness Tc (as shown in FIG.22A) within a range of from 0.0005 μm to 10000 μm, such as a thicknesswithin a range of from 0.005-10000 μm, 0.005-1000 μm, 0.005-500 μm,0.01-500 μm, 0.01-100 μm, 0.02-100 μm, 0.05-100 μm, 0.05-50 μm, 0.05-10μm, or 0.05-5 μm. In some embodiments, the thickness of each conductivematerial layer is the same. By “the same” is meant that the thickness ofeach layer varies by less than ±5% relative to an average thickness ofthe layers, such by less than ±2% relative to an average thickness ofthe layers.

Optionally, as shown in FIG. 23, the stacked CESD 2200 further includesa nonconductive sealing material 2260 in contact with one or more sideedges of the stacked arrangement 2230 and extending from the firstelectrode 2210 to the second electrode 2220. The nonconductive sealingmaterial may electrically isolate the stacked CESD, provide resistanceto fluid flow when using a fluid dielectric material, and/or provideadditional mechanical strength to the stacked CESD. Suitablenonconductive sealing materials include, but are not limited to,polymerized p-xylylene (e.g., Puralene™ polymer), a copolymer comprisingp-xylylene and a co-monomer, or polyethylene terephthalate. Again, thegaps shown between the layers do not exist, and are shown only toclearly distinguish the layers.

As shown in FIG. 22A, the stacked CESD has a height H, as measured froman outwardly facing surface of the first electrode to an outwardlyfacing surface of the second electrode. In some embodiments, the heightH is within a range of from 0.025 μm to 2000 μm, such as a height withina range of from 0.05-2000 μm, 0.1-2000 μm, 1-2000 μm, 1-1000 μm, 5-1000μm, 10-1000 μm, 10-500 μm, 10-200 μm, or 10-100 μm.

In some embodiments, a stacked CESD includes an array of spaced-apartelectrodes arranged in a plurality of parallel planes or layers with adielectric material filling spaces between the electrodes. FIGS. 24A-24Cshow a stacked CESD 2400 including n groups of parallel electrodesarranged in n stacked parallel planes or layers, the CESD comprisingalternating planes or layers of first electrodes 2410 and secondelectrodes 2420. FIG. 24A is a perspective view of CESD 2400, and FIGS.24B and 24C are bottom and side views, respectively. The dotted linesindicate a unit cell 2401. Each electrode 2410, 2420 has a central axisAc parallel to the plane in which the electrode is located. In theexemplary CESD of FIG. 24, electrodes 2410 and 2420 have opposingpolarities during use. Each electrode in a given layer (e.g., allelectrodes 2410 in a given layer) have the same polarity during use. Adielectric material 2430 occupies the spaces between the electrodes2410, 2420 and contacts the electrodes. Regions of the dielectricmaterial 2430 located between adjacent electrodes 2410, 2420 of opposingpolarities define capacitive elements 2435. Electrodes 2410 in any givenlayer are vertically aligned with electrodes 2410 in other layers.Electrodes 2420 in any given layer are vertically aligned withelectrodes 2420 in other layers. In some embodiments, the CESD 2400 hasa quadrilateral configuration defining four side edges of the CESD.Advantageously, one end of each electrode (e.g., electrode ends 2412,2422) protrudes from the dielectric material 2430 at one side edge ofthe CESD such that electrical connections can be made. In certainembodiments, a conductive material (not shown) is applied to twoadjacent side edges, e.g., side edges A and B, of the CESD 2400 suchthat protruding ends 2412 are in contact with and electrically connectedin parallel with the conductive material on one side edge of the CESD2400 and protruding ends 2422 are in contact with and electricallyconnected in parallel with the conductive material on an adjacent sideedge of the CESD 2400. During use, the conductive material on one sideedge of the CESD is connected to a voltage source, and the conductivematerial on the adjacent side edge of the CESD is connected to Vss.

In an independent embodiment, electrodes in a lowermost layer of theCESD 2400, e.g., electrodes 2410 in the lowermost layer are connected inseries with an electrical interconnect 2440; electrodes in an uppermostlayer of the CESD 2400, e.g., electrodes 2420 in the uppermost layer,are connected in series with an electrical interconnect 2450.

In one embodiment, electrodes of a given polarity from two or morelayers are connected in series, e.g., vertically aligned electrodes 2420are serially connected using an electrical interconnect 2440. In anotherembodiment, electrodes in a given layer (i.e., horizontally alignedelectrodes of a given polarity) are serially connected using anelectrical interconnect 2450.

In the exemplary CESD of FIG. 24, electrodes 2420 are oriented at rightangles to electrodes 2410. However, a perpendicular orientation is notrequired. FIG. 25 shows a stacked CESD 2400 a including n groups ofparallel electrodes arranged in n stacked parallel planes or layers, theCESD comprising alternating layers of first electrodes 2410 a and secondelectrodes 2420 a. Each electrode 2410 a, 2420 a has a central axis Acparallel to the plane in which the electrode is located. A dielectricmaterial 2430 a occupies the spaces between the electrodes 2410 a, 2420a and contacts the electrodes. Electrodes 2410 a and 2420 a haveopposing polarities during use. Regions of the dielectric material 2430a located between adjacent electrodes of opposing polarities definecapacitive elements 2435 a. The electrodes 2410 a and 2420 a are notoriented at right angles to one another. In contrast, electrodes 2420 aare rotated from 90° relative to electrodes 2410 a. In FIG. 25, therotation is 30° from right angles. The degree of rotation is not limitedto 30°, however. The degree of rotation may be, for example, within arange of 0-90°, 0-45°, 5-45°, 10-45°, 15-40°, or 20-35°, such as adegree of rotation of 0°, 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40°, or 45°.Furthermore, although the orientation of each layer of electrodes 2410 ais the same and the orientation of each layer of electrodes 2420 a isthe same in the exemplary CESD 2400 a of FIG. 24, the configuration isnot so limited. Indeed each successive layer of electrodes may berotated relative to the plane directly below, thereby producing atwisting spiral configuration of the electrodes (not shown).

FIGS. 26A-26D show a stacked CESD 2600 including n groups of parallelelectrodes arranged in n stacked parallel planes or layers, the CESDcomprising planes or layers of electrodes 2610, 2620. FIG. 26A is aperspective view of CESD 2600, FIG. 26B is a bottom view, and FIGS. 26Cand 26D are side views with offset and vertically aligned electrodes,respectively. The dotted lines indicate a unit cell 2601. Each electrode2610, 2620 has a central axis Ac parallel to the plane in which theelectrode is located. A dielectric material 2630 occupies the spacesbetween the electrodes 2610, 2620 and contacts the electrodes.Electrodes 2610, 2620 have opposing polarities during use. Regions ofthe dielectric material 2630 located between adjacent electrodes ofopposing polarities define capacitive elements 2635. In each layer,electrodes 2610 alternate with electrodes 2620. Thus, each layerincludes electrodes of alternating polarities. The CESD 2600 may have aquadrilateral configuration defining four side edges A, B, C, D.Advantageously, one end of each electrode, e.g., electrode ends 2612,2622, protrudes from the dielectric material 2630 at one side edge suchthat electrical connections can be made. Because the electrodesalternate in polarity in each layer, electrode ends 2612, 2622 protrudefrom opposing sides of the CESD 2600, e.g., sides A, C. Similarly,electrode ends 2614, 2624 protrude from the two remaining opposing sidesof the CESD 2600, e.g., sides B, D. In some embodiments, a conductivematerial is applied to each of the four side edges of the CESD 2600 suchthat protruding electrode ends of each side edge are in contact with andelectrically connected in parallel with the conductive material on thatside edge. The conductive material on two adjacent side edges isconnected to a voltage source, and the conductive material on the tworemaining side edges is connected to Vss, e.g., ground. For example, theconductive materials in contact with electrode ends 2612, 2614 may beconnected to a voltage source and the conductive materials in contactwith electrode ends 2622, 2624 may be connected to Vss. Alternatively,an electrical interconnect on one side edge of the CESD can be used toserially connect electrodes of a given polarity in a particular plane,and an electrical interconnect on the opposing side edge of the CESD canbe used to serially connect electrodes having the opposite polarity inthat particular plane.

In the stacked CESD 2600 as illustrated in FIGS. 26A and 26C, there is aplane/plane offset such that electrodes in the alternating layers withthe same orientation, e.g., electrodes in the first and third layers orelectrodes in the second and fourth layers, are not vertically alignedwith one another. However, in some examples, there may be no offset suchthat the electrodes in alternating layers with the same orientation arevertically aligned with one another (FIG. 26D). In the exemplaryembodiment of FIG. 26, electrodes in each layer are oriented at rightangles to electrodes in adjacent layers. However, as described abovewith respect to CESD 2400 a (FIG. 25), the electrodes in any layer maybe rotated from 0-90° relative to electrodes in the adjacent layers. Thedegree of rotation may be, for example, within a range of 0-45°, 5-45°10-45°, 15-40°, or 20-35°, such as a degree of rotation of 0°, 5°, 10°,15°, 20°, 25°, 30°, 35°, 40°, or 45°. Furthermore, each successive layerof electrodes may be rotated relative to the plane directly below,thereby producing a twisting spiral configuration of the electrodes (notshown).

Although the electrodes 2410, 2410 a, 2420, 2420 a, 2610, and 2620 inFIGS. 24-26 are illustrated as having a right cylindrical configuration,it is to be understood that the electrodes alternatively may have acomplex surface geometry. For example, the electrodes may have across-sectional area that is semi-circular, elliptical or polygonal. Asanother example, the electrodes may have a regular or smooth surface, oran irregular or rough surface.

In still other examples, the electrodes may be twisted or sinuous wiresor traces. FIG. 27A shows a plurality of parallel, twisted or sinuouselectrodes 2710 which may be used in the foregoing embodiments. Byparallel is meant that the curves in adjacent electrodes are in phasewith one another. For instance, if the x-axis extends along the lengthof the electrode 2710, and the curves have a positive or negativeamplitude with respect to the x-axis, then the apices A (i.e., points ofmaximum deviation) of the curves of any two adjacent electrodes at anygiven distance along the x-axis have the same direction from the x-axis.The curves may deviate from the x-axis in the y-direction or thez-direction. In some embodiments, the curves of any two adjacentelectrodes at any given distance along the x-axis have the same, orsubstantially the same, amplitude and direction from the x-axis suchthat the distance D between the adjacent electrodes is the same, orsubstantially the same along the length of the x-axis. Each of theelectrodes 2710 has the same polarity. FIG. 27B shows another parallelarrangement in which alternating electrodes 2710, 2720 have oppositepolarities.

FIG. 28A shows an antiparallel arrangement including a plurality oftwisted or sinuous electrodes 2710, wherein each of the electrodes 2710has the same polarity. By antiparallel is meant that the curves inadjacent electrodes are out of phase with one another, such as 180° outof phase. For instance, if the x-axis extends along the length of theelectrode 2710, and the curves have a positive or negative amplitudewith respect to the x-axis, then the curves of any two adjacentelectrodes at any given distance along the x-axis have oppositedirections from the x-axis. The curves may deviate from the x-axis inthe y-direction or the z-direction. In some embodiments, the apices ofthe curves of any two adjacent electrodes at any given distance alongthe x-axis have the same, or substantially the same, amplitude butopposite directions from the x-axis such that the distance between theadjacent electrodes varies from a maximum distance D₁ to a minimumdistance D2 along the length of the x-axis. FIG. 28B shows anotherantiparallel arrangement in which alternating electrodes 2710, 2720 haveopposite polarities. An increased E-field may be produced where theelectrodes are in closer proximity to one another. The energy storage inthese areas is larger due to increases in the E-field and its shape.

In further examples, a sinuous wire-type electrode may be formed with awire including periodic protrusions or bumps along the electrode'ssurface. FIG. 29A shows a plurality of parallel electrodes 2910, eachelectrode 2910 including periodic protrusions 2912 along the length ofthe electrode. Each of the electrodes 2910 has the same polarity. FIG.29B shows another parallel arrangement in which alternating electrodes2910 with periodic protrusions 2912 and electrodes 2920 with periodicprotrusions 2922 have opposite polarities. FIG. 30A shows anantiparallel arrangement in which each of the electrodes 2910 has thesame polarity. FIG. 30B shows another antiparallel arrangement in whichalternating electrodes 2910, 2920 have opposite polarities.

A person of ordinary skill in the art understands that the stacked CESDsexemplified in FIGS. 24-26 may further include edge connectors (notshown, but similar in nature to edge connectors 2215, 2225 of FIG. 23)for external connections to the electrodes and/or a nonconductivesealing material (not shown, but similar in nature to nonconductivesealing material 2260 of FIG. 23) in contact with one or more side edgesof the stacked arrangement. The stacked CESD may further include anonconductive sealing material on the upper and lower surfaces of thestacked CESD (not shown). The nonconductive sealing material mayelectrically isolate the stacked CESD, provide resistance to fluid flowwhen using a fluid dielectric material, and/or provide additionalmechanical strength to the stacked CESD. Suitable nonconductive sealingmaterials include, but are not limited to, polymerized p-xylylene (e.g.,Puralene™ polymer), a copolymer comprising p-xylylene and a co-monomer,or polyethylene terephthalate.

Electrical connections to the stacked CESDs of FIGS. 24-26 may be madein different ways. In some instances, electrical connections to theappropriate polarities are made only to the uppermost and lowermostlayers of electrodes, and the inner layers are allowed to “float.”However, the number of layers would be limited as the overall voltageacross the device would increase to very high values. Alternatively,individual layers of electrodes may be connected to their correspondingpolarities in a perpendicular plane or in multiple perpendicular planes.Edge connections have several advantages, including that the individualelectrodes will have lower resistance and impedance connections to theflowing electrical charges and the CESDs will be relatively easy toconnect with larger dimensionality. To facilitate edge connections, agiven polarity of electrodes are allowed to protrude from a given sidemore than electrodes of the opposite polarity. In this way, a conductivematerial can be applied to that entire side to make parallel electricalconnections between the individual electrodes and an electrical bus.Other sides of the stacked CESD can be treated similarly. When eachlayer of the stacked CESD includes electrodes with alternatingpolarities, two opposing sides of the CESD will be used to make theconnections. The two remaining sides will be used for electricalconnections to electrodes in the adjacent planes, which have a differentorientation as illustrated in FIGS. 24-26.

FIG. 31 illustrates a cross-section of an exemplary tubular stacked CESD3100 having a cylindrical configuration. Apparent gaps between elementsof the stacked CESD 3100 are shown for clarity purposes only and are notpresent in the actual device. In the embodiment of FIG. 31, the firstelectrode 3110 has a cylindrical configuration, an inwardly facingsurface 3110 a, an outwardly facing surface 3110 b, and an outerdiameter D₁. The first electrode 3110 may be a hollow tube, such as ahollow metal tube as shown. Alternatively, the first electrode 3110 maybe a solid tube, such as a metal solid tube (not shown). It isunderstood that when the first electrode 3110 is a solid tube, theelectrode does not have an inwardly facing surface. The second electrode3120 has a cylindrical configuration, an inwardly facing surface 3120 a,an outwardly facing surface 3120 b, and an inner diameter D2, whereinthe inner diameter D2 is greater than the outer diameter D₁ of the firstelectrode 3110. The first and second electrodes 3110, 3120 are arrangedsuch that the first electrode 3110 is positioned within a space definedby the inwardly facing surface 3120 a of the second electrode 3120.

A stacked arrangement comprising alternating layers of dielectricmaterial and conductive material is disposed between the outwardlyfacing surface of the first electrode and the inwardly facing surface ofthe second electrode in concentric alternating layers of the dielectricmaterial and the conductive material. The stacked arrangement includes xlayers of the dielectric material, wherein (i) x is an integer greaterthan or equal to two, (ii) a first layer of the dielectric material 3140a is in direct contact with the outwardly facing surface 3110 b of thefirst electrode 3110, and (iii) layer x of the dielectric material 3140x is in direct contact with the inwardly facing surface 3120 a of thesecond electrode 3120. The stacked arrangement further comprises ylayers of the conductive material, wherein y=x−1 and a layer of theconductive material is positioned between each pair of adjacent layersof the dielectric material. The dielectric and conductive materials areas previously described.

Embodiments of the tubular stacked CESD 3100 include x layers of thedielectric material 3140, wherein x is an integer greater than or equalto two, and y layers of the conductive material 3150, wherein y=x−1.From a theoretical standpoint, the number of layers is essentiallyunlimited. However, the number of layers may be practically limited bymanufacturing constraints (e.g., difficulty in forming many layershaving a reproducible thickness). In some embodiments, x is an integerfrom 2-5000, 2-1000, 2-500 2-100, 2-50, 2-25, 2-10, or 2-5. For example,x may be 2, 3, 4, 5, 6, 7, 8, 9, or 10. In such arrangements, y is 1, 2,3, 4, 5, 6, 7, 8, or 9, respectively. In the nonlimiting exemplarystacked CESD of FIG. 31, x is 3 and y is 2.

Optionally, the tubular stacked CESD 3100 further comprises an outernonconductive sealing material 3160 in contact with the outwardly facingsurface 3120 b of the second electrode 3120, as shown in FIG. 32. Ifdesired, the outer nonconductive sealing material may be applied to allexterior surfaces of the tubular stacked CESD 3100. The outernonconductive sealing material may electrically isolate the tubularstacked CESD, provide resistance to fluid flow when using a fluiddielectric material, and/or provide additional mechanical strength tothe tubular stacked CESD. Suitable nonconductive sealing materialsinclude, but are not limited to, polymerized p-xylylene (e.g., Puralene™polymer), a copolymer comprising p-xylylene and a co-monomer,polyethylene terephthalate, shellac, polyurethane, or cross-linkedpolyurethane.

Advantageously, embodiments of the disclosed stacked CESDS asillustrated in FIGS. 22A, 22B, 31, and 32 function similarly to aplurality of serially-connected capacitors, thereby allowing use ofhigher voltages than would otherwise be suitable for conventionalcapacitors. With reference to FIGS. 22A and 22B, a voltage appliedbetween the first and second electrodes 2210, 2220 is divided across thestack. When the layers of dielectric material have the same thickness,the voltage is evenly divided. Thus, if an exemplary voltage of 5V isapplied across the stacked CESD 2200, a 1V drop will be observed acrosseach of the five dielectric material layers 2240. Stacking increases thedimensionality of the CESD while retaining the ability to apply a highvoltage to each conductive layer in the stack without having to makeelectrical connections to each individual layer. This feature allowshigher voltages to be applied to the stacked CESD without resultingdielectric breakdown, as compared to voltages that can be applied to acapacitor including a single layer of dielectric material. Furthermore,embodiments of the disclosed stacked CESDs exhibit very littledetectable leakage after being charged and may hold a charge for agreatly extended period of time compared to known electrolyticcapacitors.

The electrodes in any or all of the foregoing embodiments may be anyconductive material. Exemplary materials include, but are not limitedto, conductive carbon, a conductive organic material other than carbon,a conductive metal, or a semiconductor.

In general, two or more of the disclosed CESDs may be connected seriallyor in parallel as would be understood by a person of ordinary skill inthe art of electrical circuits. Tubular CESDs as shown in FIGS. 20 and21, however, typically are connected in parallel to provide atwo-connection device. Serial and/or parallel connections of CESDs maybe made at the time of manufacture or subsequently by an end user.

Selective switching of electrical connections to capacitive elements ofa CESD allows combinations of the capacitive elements for use incomputational devices. As shown in FIG. 33, individual capacitiveelements may be concatenated in series or in parallel configurations,providing additive/subtractive, or averaged voltages, respectively. Forexample, in a stacked CESD, switches may be set to activate two adjacentelectrodes in a first layer of electrodes, thereby applying a voltageacross one or more capacitive elements between the two adjacentelectrodes of the first layer. Additional switches may be set toactivate another two adjacent electrodes in another region of the firstlayer or in another layer of electrodes in the CESD stack, therebyapplying a voltage across one or more capacitive elements in the otherregion or layer. The switches may be externally connected in a desiredconfiguration, e.g., in series or parallel, to combine the outputs asdesired by methods well known to those skilled in the art of electricalcircuitry and/or computational devices. These electrical connections areused to perform mathematical operations, and may be utilized directly asmemory storage of a device to perform logical operations and computationas well as compression of stored data.

FIG. 34 illustrates exemplary connections of two capacitiveelements—series additive, series additive inverted, series subtractive,series subtractive inverted, and parallel average. A person of ordinaryskill in the art understands that the illustrated concepts can beexpanded to sets of multiple capacitive elements, thereby extending thecommands to n x m elements. Concatenation of the operators can be usedto provide new operators that can be configured and used within a singleoperational cycle. For example, extended numerical division can beperformed using the ability to divide arrays of capacitive elements intoother arrays simultaneously to provide division with essentiallyunlimited precision in a two-cycle operation. Basic operators include:ADD(n)—add n elements to give a sum (adding two elements also can be alogical AND or NAND); ADDI(n)—add n elements to give a negative sum;DIV(n,m)—divide n elements by m elements; SUB(n,m)—subtract element nfrom element m (subtracting two elements can be a logical OR or NOR);SUBI(n,m)—subtract element m from element n; AVE(n)—provides theaveraged output of n elements; SFL(n)—shift left n elements;SFR(n)—shift right n elements. Table 2 shows resulting output voltagesfrom several exemplary combinations of the capacitive elements asillustrated in FIG. 34:

TABLE 2 Output Voltages Initial Charge Series Series Voltages SeriesAdditive Series Subtractive Parallel V1 V2 additive Inverted SubtractiveInverted Average 0 0 0 0 0 0 0 0 1 1 1 −1 1 0.5 1 0 1 −1 1 −1 0.5 1 1 20 0 0 1 Threshold OR (0.5) XOR (<>0) XOR (<>0) XOR (<>0) OR (0.25)Voltages( ) AND (1.5) AND (0.75)

Parallel connections can be used to perform multi-element logicoperators on arrays. The voltage averaging that occurs can be used toreduce the overall voltage on the outputs to maintain common digitalvoltage levels. In some embodiments, a sense amplifier and/or acomparator may be used to decode voltages produced by connectedcapacitive elements. Advantageously, embodiments of the disclosed CESDsand CESD stacks may be used to manufacture computers capable ofperforming logical operations and computations much faster thanconventional computers, such as up to 100× or 200× faster thanconventional computers.

In some embodiments, a CESD functions as both an energy storage deviceand a memory device. With reference, for example, to FIGS. 10 and 11, anedge row group of electrodes and all column groups including anelectrode in the edge row may be activated to charge all capacitiveelements between electrodes of the edge row and store energy. Individualelectrodes elsewhere in the CESD can be addressed to read and write toone or more capacitive elements for memory storage. As illustratedschematically in FIG. 19, a switching array 310 and controller 320comprising a logic circuit may be used to operate the CESD.

III. Dielectric and Insulative Materials

Embodiments of the disclosed CESDs comprise a dielectric material havinga relative permittivity greater than silicon dioxide, i.e., greater than3.9. In some embodiments, the dielectric material has liquidcharacteristics, and has a viscosity similar to honey or greater. Incertain embodiments, the dielectric material has a viscosity greaterthan or equal to 0.5 cP, such as a viscosity from 10,000 cP to 250,000cP. In an independent embodiment, the dielectric material is a solid.

The dielectric material may be substantially free of conductivity; inother words, the dielectric material does not undergooxidation/reduction at or near the electrodes and does not exhibit Ohmicconductivity. In other embodiments, the dielectric material isconductive. The dielectric material may comprise a conductive ornonconductive polymer, an inorganic metal oxide, mixed metal oxides,mixed polymer and organic materials, or combinations thereof. In someexamples, the polymer is a biopolymer.

In some embodiments, the dielectric material comprises polymericmolecules having polar and/or ionizable functional groups, resulting inintramolecular dipoles and dipole moments. The polymeric molecules mayfurther include one or more double bonds. In some embodiments, thepolymeric molecules are polar polymers. Proteins are readily available,inexpensive polar polymers that have low toxicity. The low toxicity is alarge advantage over other polymers, and allows the CESDs to be recycledor incinerated. A protein molecule includes amino acids with polarand/or ionizable functional groups. Other suitable polymers include, butare not limited to, substituted (e.g., fluorinated) and unsubstitutedparylene polymers, polypropylene, acrylic acid polymers, methacrylicpolymers, polyethylene glycol, urethane polymers, epoxy polymers,silicone polymers, organic terpenoid polymers, natural organic polymers(e.g., resins such as shellac), polyisocyanates, and combinationsthereof. Copolymers, such as acrylate copolymers (e.g., copolymers withethylene butyl-, ethyl-, and methyl-acrylates) and parylene copolymers(e.g., copolymers of p-xylylene with acrylates (e.g., 2-carboxylethylacrylate), methacrylates (e.g., 3-(trimethoxysilyl)propyl methacrylate),α-pinene, R-(−)carvone, linalool, cyclohexene, dipentene, α-terpinene,R-(+)-limonene, and combinations thereof), also are within the scope ofthis disclosure. Non-limiting examples of polar polymers include zein,hemp protein, wheat gluten, poly(acrylic acid-co-maleic acid),poly(acrylic acid), whey protein isolate, soy protein isolate, peaprotein extract, shellac, and combinations thereof.

In certain embodiments, polymeric molecules are derivatized to attachadditional functional groups, such as functional groups that facilitatesubsequent binding of the polymeric molecules to a bare electrodesurface (i.e., a bare metal or carbon surface) or to a compositeelectrode surface. Exemplary derivatization agents include, but are notlimited to, anhydrides, carbodiimides, imidoesters, and reagentsincluding combinations of N-hydroxysuccinimide and maleimide, arylazide, or diazirine groups. In some examples, the polymer is derivatizedwith an anhydride, such as maleic anhydride, itaconic anhydride,cis-4-cyclohexene-1,2-dicarboxylic anhydride, orcis-5-norbornene-end-2,3-dicarboxylic anhydride. A derivatized polymericmolecule can be bound to the electrode surface by crosslinking or byother reaction with the surface. A polymeric molecule also can becrosslinked with one or more other polymeric molecules in thedielectric. When a polymeric molecule is derivatized with maleicanhydride, for example, the derivatized polymeric molecule can becrosslinked through the double bonds. Crosslinking can be performed byany suitable means, such as a chemical agent (e.g., a radicalinitiator), ultraviolet light activation, or thermal activation. Twonon-limiting examples of nonconductive, high-permittivity dielectricsare zein in a shellac matrix and a protein derivatized with maleicanhydride.

The inventors surprisingly discovered that polymeric molecules with theabove-described characteristics, when sterically constrained, can beused for energy storage even though the polymeric molecules cannotfreely move between opposing electrodes. Polymeric molecules can besterically constrained by binding the polymeric molecules to a bareelectrode surface or to a nonconductive or insulative coating of acomposite electrode by any means, including a covalent bond (single ormultiple), van der Waals forces, or hydrogen bonding, prior to chargingand/or discharging an energy storage device including the electrode anda dielectric material comprising the polymeric molecules.

Without wishing to be bound by any particular theory of operation, it isbelieved that within a large molecule, movements of only portions of themolecule may take place while other portions of the molecule are boundin place sufficiently to prevent the overall movement to a lower energylevel and subsequent release of potential energy to be coupled to theelectrode and not released as thermal motion. This constraint ofmovement decreases the degrees of freedom in the dielectric molecule,and consequently decreases the molecule's ability to dissipate absorbedenergy from the electrical field as heat. Thus, a bound polymericmolecule couples to the electric field in such a way that the polymericmolecule cannot release energy in the form of heat due its reduceddegrees of freedom. The movement of certain portions of a macromoleculecan be related and is similar to electrophoretic movements known tothose who use such techniques to analyze biological macromolecules.

Additionally, without wishing to be bound by any particular theory ofoperation, it is believed that when a portion of the polymer is bound toan electrode (or to a coating on the electrode), the remainder of thepolymer may stretch, twist, or bend within the dielectric film as polarand/or ionizable functional groups reorient in response to an electricfield. These changes in conformation and position store energy withinthe energy storage device. When the energy storage device discharges,the stored energy is released as electrical energy as the bound polymermolecules return to a less ordered conformation. A dielectric materialcomprising polymeric molecules, wherein at least some of the polymericmolecules have decreased degrees of freedom, is referred to as a“sterically constrained” dielectric material.

In some embodiments, the dielectric material comprises an organicpolymer and a high permittivity compound, such as an inorganic salt or asalt comprising a metal cation and an organic anion. The dielectricmaterial may further include a solvent. Suitable polymers include, butare not limited to, zein, shellac, and silicone oil. In someembodiments, the salt comprises a group IIA or group IIIA metal. In oneembodiment, the inorganic salt is a boron compound, such as sodiumborohydride or borax. When the inorganic salt is sodium borohydride orborax, the dielectric material may further comprise ammonium hydroxide.In an independent embodiment, the inorganic salt is barium titanate. Inanother independent embodiment, the inorganic salt is a Gd, Sr, or Snsalt. In still another independent embodiment, the inorganic salt is atransition metal salt, such as an iron salt. The salt may be, forexample, a carbonate salt. When the inorganic salt is barium titanate ora transition metal salt, the dielectric material may further comprisesodium borohydride or borax. In certain embodiments, the dielectricmaterial further comprises a permittivity increasing material orbreakdown voltage adjuvant. The permittivity increasing material orbreakdown voltage adjuvant may include Y, Ni, Sm, Sc, Tb, Yb, La, Te,Ti, Zr, Ge, Mg, Pb, Hf, Cu, Ta, Nb, Bi, or a combination thereof, whichis substantially evenly distributed throughout the material.

In certain examples, the dielectric material comprises a zein proteinderivatized with maleic anhydride and neutralized with a carbonate salt.

In some embodiments, the dielectric material has a relative permittivitygreater than silicon dioxide, i.e., greater than 3.9. In certainembodiments, the dielectric material has liquid characteristics, and hasa viscosity similar to honey or greater. The dielectric material mayhave a viscosity greater than or equal to 0.5 cP, such as a viscosityfrom 0.5 cP to 250,000 cP, 10 cP to 250,000 cP, 100 cP to 250,000 cP,500 cP to 250,000 cP, 1,000 cP to 250,000 cP, 5,000 cP to 250,000 cP, or10,000 cP to 250,000 cP.

In some embodiments, the dielectric material is an electroentropicdielectric material having a relative permittivity greater than 3.9 asdisclosed herein. The electroentropic dielectric material may comprise aplurality of polymeric molecules as previously described. In someexamples, the polymeric molecules comprise proteins, polyp-xylylene)poly(maleic acid), acrylic acid polymers, methacrylic acid polymers,polyethylene glycol, urethane polymers, epoxy polymers, siliconepolymers, terpenoid polymers, naturally occurring resin polymers,polyisocyanates, or combinations thereof. In certain CESDs, thepolymeric molecules are poly(p-xylylene), zein, poly(maleic acid),shellac, silicone oil, or a combination thereof.

Each dielectric material layer may have a thickness T_(D) (as shown inFIG. 22A) within a range of from 0.0001 μm to 10000 μm, such as athickness within a range of 0.0005-10000 μm, 0.0005-1000 μm, 0.0005-100μm, 0.001-100 μm, 0.01-100 μm, 0.05-100 μm, 0.1-50 μm, 0.5-10 μm, or 1-5μm. In some embodiments, the thickness of each dielectric material layeris the same. By “the same” is meant that the thickness of each layervaries by less than ±5% relative to an average thickness of the layers,such by less than ±2% relative to an average thickness of the layers.

The conductive material comprises a carbonaceous material, a metal, aconductive polymer, or a combination thereof. Carbonaceous materialsinclude any conductive material comprising conductive carbon including,but not limited to, carbon powder, graphene, graphitic carbon,graphitized carbon, partially graphitized carbon (e.g., a graphitic-typestructure content within a range of from 20 to 99 wt %), activatedcarbon, carbon black, and carbonized polymers (polymers converted atleast partially into carbon or a carbon-containing residue, typically bypyrolysis or chemical treatment), or any combination thereof. Suitablemetals include, but are not limited to, aluminum, copper, gold,platinum, silver, titanium, and combinations thereof. In certainexamples, the conductive material comprises or consists of carbonpowder, graphene, graphite, aluminum, polyaniline, or poly(N-methylpyrrole).

Additional disclosure regarding suitable dielectric materials is found,e.g., in U.S. Pat. Nos. 8,432,663, 8,940,850, 9,011,627, US2015/0000090A1, US 2015/0000833 A1, and US 2015/0131198 A1, each ofwhich is incorporated in its entirety herein by reference.

As described above, a CESD may include one or more insulative layersbetween electrical connects. Electrodes and/or an underlying substratealso may have an insulative layer or coating. The CESD may furthercomprise an upper sealing layer. The insulative layer and/or sealinglayer may have an Ohmic conductivity less than 1×10⁻¹ S/m. In someembodiments, the insulative layer has an Ohmic conductivity less than1×10⁻² S/m, less than 1×10⁻⁵ S/m, or less than 1×10⁻¹° S/m. In certainembodiments, the Ohmic conductivity is from 1×10⁻²⁵ S/m to 1×10⁻¹ S/m,from 1×10⁻¹° S/m to 1×10⁻¹ S/m or from 1×10⁻⁵ S/m to 1×10⁻¹ S/m. Theinsulative layer may range from a few nanometers to greater than 50microns in thickness. In some embodiments, the insulative layer has anaverage thickness from 5 nm to 10 μm, such as from 0.1-10 μm, 0.3-10 μm,0.3-5 μm, or 0.3-2 μm. The sealing layer may have an average thicknessfrom 50 nm to 50 mm, such as from 50 nm to 25 mm, or from 100 nm to 10mm.

An exemplary insulative or sealing layer is polymerized p-xylylene, suchas a Puralene™ polymer coating as disclosed, for example, in US2014/0139974, which is incorporated in its entirety herein by reference.The insulative layer may be modified with appropriate co-monomers toprovide increased permittivity, and/or attachment sites for polymericmolecules of the dielectric material. In some embodiments, theco-monomers include one or more unsaturated bonds. An insulative layercomprising polymerized p-xylylene may be modified, for example, byinclusion of co-monomers including, but not limited to, olefins, vinylderivatives, alkynyl derivatives, acryl compounds, allyl compounds,carbonyls, cyclic ethers, cyclic acetals, cyclic amides, oxazolines, andcombinations thereof. In some embodiments, the co-monomers are acrylates(e.g., 2-carboxylethyl acrylate), methacrylates (e.g.,3-(trimethoxysilyl)propyl methacrylate), α-pinene, R-(−)carvone,linalool, cyclohexene, dipentene, α-terpinene, R-(+)-limonene, andcombinations thereof. The copolymers may include alternating monomers ormay be in the form of block copolymers.

IV. Methods of Making a CESD

As shown in the flow diagram of FIG. 35, some embodiments of a methodfor making a CESD as disclosed in FIGS. 2-18 comprise forming an arrayof electrodes at least partially embedded within or in contact with adielectric material with spaces between the electrodes, the array ofelectrodes comprising n groups of electrodes arranged in a single plane,where n is an integer greater than or equal to 2, each electrode havinga central axis perpendicular to the plane (step 3501); and connectingelectrodes of each group in series with an electrical interconnect,thereby forming the CESD (step 3502).

In some embodiments, forming the array of electrodes at least partiallyembedded in or in contact with the dielectric material further comprisesforming the array of electrodes (step 3501 a), and then disposing thedielectric material in the spaces between the electrodes (step 3501 b).The electrodes may be formed by any suitable means including, but notlimited to, forming the electrodes on a substrate by nanolithography,microlithography, shadow-mask polymerization, laser marking, imprint,inkjet, grauver, flexographic, or a screen printing process. In oneembodiment, the substrate is a nonconductive surface; in anotherembodiment, the substrate is a removable carrier. In certainembodiments, the array of electrodes is formed using nanolithography,such as roll-to-roll (R2R) nanoimprint lithography (NIL) where anelectrode material layered on a flexible substrate is rolled withpressure over a rigid stamp, which patterns the electrode material toform the array of electrodes (see, e.g., Kooy et al., Nanoscale ResearchLetters 2014, 9:320). Advantageously, R2R NIL provides a solution todevice manufacture that does not need vacuum processing. In analternative method, vacuum processes, such as those well-known for themanufacture of microelectronics can be used to form the array ofelectrodes. Alternative methods such as simple photolithographyutilizing shadow masks are also possible. The advantages of anon-contact process such as photolithography at longer wavelengths thanvacuum ultraviolet are clear advantages. These advantages when coupledwith the lack of a need for vacuum process, make a compelling argumentfor the economic manufacturing methods of this invention. In oneembodiment, the electrodes are metal, and are anodized by methods wellknown to those skilled in the art of capacitor production. In anindependent embodiment, the electrodes are coated with an insulativelayer or coating, such as a Puralene® polymer (poly-p-xylylene) coating.Methods for forming a Puralene® polymer (poly-p-xylylene) coating andsimilar coatings are further described in U.S. Pat. No. 8,633,289 and US2015/0017342 A1, each which is incorporated in its entirety herein byreference. A polyp-xylylene) insulative coating on the electrodes may beformed in the presence of an electric field or a magnetic field. In oneembodiment, the insulative coating is formed in the presence of a directcurrent electric field greater than 100 V/cm. The substrate/carrier andelectrodes may, for example, be immersed in a direct current electricfield as the insulative coating is applied to the electrodes. In anotherembodiment, the insulative coating is formed in a magnetic field greaterthan 1 Gauss, wherein the magnetic field may be provided by placing thesubstrate/carrier and electrodes between magnetic north and south polesof a magnetic source while applying the insulative coating. Theelectrode material may also be provided by electrode plating methods orspatial atomic layer deposition (ALD).

The dielectric material may be disposed in the spaces between theelectrodes by any suitable means including, but not limited to, flowinga solvent-based dielectric, such as a viscous dielectric, onto thesubstrate, spraying the dielectric onto the substrate, vapor-phasedeposition, or other methods known to those skilled in the art of filmformation. In some instances the dielectric is solidified, e.g., byremoving solvent, such as by evaporation, or by cross-linking polymersin the dielectric material. A removable carrier may be subsequentlyremoved by any suitable method. For example, a removable carriercomprising a water-soluble polymer can be dissolved and removed withwater.

In an alternative method, a layer of dielectric material is formed on asubstrate (e.g., by vapor phase deposition, liquid spraying, screening,spin-coating, pressing, or other methods known to those of skilled inthe art of film formation) (step 3501 c), and electrodes are at leastpartially embedded in or placed in contact with the dielectric materialto form the array of electrodes (step 3501 d). In some embodiments, alayer of dielectric material is applied to a substrate or removablecarrier film. If liquid, the dielectric film may be partially dried atlow temperatures (e.g., 25-60° C.) before proceeding. In anotherindependent embodiment, a layer of dielectric material is pressed onto aconductive surface to act as a masking layer. The dielectric materialcan serve as both the substrate and an insulative layer, as well as themedium for energy storage. In certain embodiments, the dielectricmaterial is patterned, e.g., by nanoimprint lithography, such as R2RNIL, or laser or chemical etching such as through a photoresist mask.Cavities in the patterned dielectric material are then filled with asuitable electrode material. In an independent embodiment, pre-formedelectrodes are inserted into the dielectric layer, e.g., while thedielectric material is in a viscous liquid or semisolid state. Inanother independent embodiment, electrodes (e.g., carbon electrodes) maybe generated in situ in or on the dielectric material using suitablechemical reactions on the surface. Graphene and other carbon inks suchas graphene oxide ink and sintering methods may also be alternativemethods for forming the conductive electrodes and interconnects.

The shape of the electrode from the manufacturing processes may becylindrical in nature or the electrodes may be flattened cylinders orother geometrical shapes due to the pressing, forming, or etchingprocess. Curved electrode surfaces may have complex spacing andgeometrical considerations especially when the paired electrodes areessentially oriented parallel or perpendicular to each other. Angledorientations may have advantages when high density capacitance or unitcell addressing on single layers is desired.

In some embodiments, the dielectric material is an entropic material,such as an electroentropic material comprising polymeric molecules, andthe film material is prepared from a liquid or a slurry comprising asolvent and a plurality of polymeric molecules. Suitable solventsinclude, but are not limited to, alkanols, alkylene glycols, lactones,carbonates, water, and combinations thereof. Exemplary solvents includeethanol, ethylene glycol, water, lactones, carbonates, and combinationsthereof. In some embodiments, the polymeric molecules have one or morepolar functional groups, ionizable functional groups, or a combinationthereof. The polymeric molecules may also include one or more doublebonds. Suitable polymeric molecules are described above. In certainembodiments, undissolved polymeric molecules are removed from themixture, e.g., by filtering or centrifuging the mixture.

The liquid or slurry may further comprise a crosslinking agent. Suitablecrosslinking agents include, but are not limited to, anhydrides,carbodiimides, imidoesters, borax salts, sodium borohydride, andreagents including combinations of N-hydroxysuccinimide and maleimide,aryl azide, or diazirine groups. Common crosslinking agents includetriallyltriazinetrione and other triallyl or trivinyl reagents known tothose versed in polymer chemistry. Exemplary anhydrides include maleicanhydride, itaconic anhydride, cis-4-cyclohexene-1,2-dicarboxylicanhydride, cis-5-norbornene-endo-2,3-dicarboxylic anhydride, andcombinations thereof.

In some embodiments, the liquid or slurry further includes an initiator,such as a radical initiator, to initialize cross-linking between thepolymeric molecules. Exemplary initiators include thermal andlight-activated chemical initiators, including, but not limited to,azobisisobutyronitrile, 1,1′-azobis(cyclohexanecarbonitrile), dicumylperoxide, 2-hydroxy-2-methylpropiophenone, camphorquinone,phenanthrenequinone, and combinations thereof. In one example, itaconicanhydride and dicumyl peroxide were used to crosslink zein molecules.

One or more salts, such as salts capable of forming organic salts withthe polymeric molecules and/or neutralizing the film material, may beadded to the liquid or slurry before crosslinking is complete. In someembodiments, a carbonate salt (e.g., guanidine carbonate, cesiumcarbonate, strontium carbonate, or a combination thereof) may be usedbecause the reaction releases carbon dioxide and produces no undesiredcounterion contamination of the dielectric film. In one embodiment,barium titanate is added to the liquid or slurry. In an independentembodiment, a voltage adjuvant, such as a nonconductive polymer, isadded.

In an independent embodiment, the polymeric molecules of the dielectricfilm are formed in situ. The dielectric material liquid or slurrycomprises a crosslinking agent and a plurality of polymeric moleculeprecursors comprising one or more polar functional groups, ionizablefunctional groups, or a combination thereof. In some examples, theprecursors are amino acid molecules, oligopeptides, polypeptides, or acombination thereof. In certain embodiments, the polymeric moleculeprecursors further comprise p-xylylene monomers. In some embodiments,the liquid or slurry is applied to the substrate or removable carrier aspreviously described. After application, the crosslinking agent isactivated, thereby crosslinking the polymeric molecule precursors toprovide a dielectric film comprising a plurality of polymeric molecules.The crosslinking process also may bind some of the polymeric moleculesto surfaces of electrodes disposed on the substrate or removable carrierlayer and/or to the substrate or removable carrier layer. In anindependent embodiment, crosslinking may be initiated prior to applyingthe liquid or slurry to the substrate or removable carrier.

Groups of electrodes are connected in series to electrical interconnectsby any suitable means. Electrical connections to the electrodes may bedirect or indirect. Direct connections can be made, for example, usingstandard wire-bonding machinery or conductive adhesives. In someembodiments, e.g., as shown in FIGS. 9-12, electrodes of one or moregroups are connected to a branched electrical interconnect by branchesextending from a main line.

In some embodiments, after the dielectric film, electrodes, andelectrical interconnects have been assembled, an electric field isapplied to the CESD. For example, a direct current electric field may beapplied by activating every other row of electrodes and grounding(connecting to Vss) the alternate rows (e.g., in the embodiments of FIG.3-6 or 15), by activating all row electrical interconnects and groundingall column electrical interconnects (e.g., in the embodiments of FIGS.7-14), or by activating one electrode while grounding the other in thecase of a co-spiral arrangement (e.g., in the embodiment of FIG. 18),such that some electrodes function as positive electrodes and othersfunction as negative electrodes. In some embodiments, an applied E-fieldin the range of from 0.0001 V/μm to 1000 V/μm or more, based on anaverage thickness of the dielectric material, is utilized. In certainembodiments, the applied E-field is within a range of 0.0001 V/μm to 100V/μm, 100 V/μm to 1000 V/μm, or 1 V/μm to 5 V/μm depending on theintended use of the CESD. The E-field is applied for an effective periodof time to bind at least some of the polymeric molecules to thepositively charged electrodes, thereby producing a stericallyconstrained dielectric film. The effective period of time is based atleast in part on the electric field strength and may range from onesecond to several minutes, such as from 30 seconds to 60 minutes, from 5minutes to 30 minutes, or from 5 minutes to 15 minutes. In someembodiments, the electric field is 0.0005-600 V/μm and the effectiveperiod of time is from 0.0001 second to 30 minutes.

In an independent embodiment, at least some of the electrodes are coatedwith an insulative layer, and a radical initiator may be applied to theelectrodes before applying the dielectric film. For example, aninsulative layer may be applied to the positive electrode or electrodes.The radical initiator may then be activated to bind at least some of thepolymeric molecules to the insulative layer and produce a stericallyconstrained dielectric film. Exemplary radical initiators includeazobisisobutyronitrile, 1,1′-azobis(cyclohexane-carbonitrile), dicumylperoxide, 2-hydroxy-2-methylpropiophenone, camphorquinone,phenanthrenequinone, combinations thereof, and other radical initiatorsknown to one skilled in the art of polymerization. The radical initiatoris activated by oxidation-reduction, photoinitiation, thermalinitiation, or other methods known to those skilled in the art ofpolymerization, thereby binding at least of the polymeric molecules tothe insulative layer on the electrodes.

In another independent embodiment, at least some of the electrodes(e.g., the positive electrode or electrodes) are coated with aninsulative layer, and polymeric molecules of the dielectric material arederivatized with a derivatization agent to provide functional groupscapable of cross-linking to the insulative layer of the electrodes. Thefunctional groups are subsequently crosslinked to the insulative layerby using a radical initiator, ultraviolet light, thermal activation, ora combination thereof, thereby producing a sterically constraineddielectric film. Exemplary derivatization agents include anhydrides,carbodiimides, imidoesters, and reagents including combinations ofN-hydroxysuccinimide and maleimide, aryl azide, or diazirine groups. Insome embodiments, the derivatization agent is an anhydride, such asmaleic anhydride, itaconic anhydride, cis-4-cyclohexene-1,2-dicarboxylicanhydride, or cis-5-norbornene-end-2,3-dicarboxylic anhydride.

With reference to FIG. 36, in embodiments where electrical interconnectsintersect one another, e.g., as shown in FIGS. 7-14, the method includesforming an array of electrodes at least partially embedded within or incontact with a dielectric material with spaces between the electrodes,the array of electrodes comprising n groups of electrodes arranged in asingle plane, where n is an integer greater than or equal to 2, eachelectrode having a central axis perpendicular to the plane (step 3601),connecting a first group of electrodes in series with a first electricalinterconnect (step 3602), and connecting a second group of electrodes inseries with a second electrical interconnect, such that there is avertical spatial separation at each intersection where the secondelectrical interconnect crosses the second interconnect (step 3603). Insome embodiments, the method includes connecting the first group ofelectrodes in series with the first electrical interconnect (step 3602a), disposing an insulative layer onto the array of electrodes and thefirst electrical interconnect such that the first electricalinterconnect is below the insulative layer (step 3602 b), disposing asecond electrical interconnect onto the insulative layer, such that thesecond electrical interconnect is positioned above the insulative layerand above the second group of electrodes (step 3602 c), and forming avia through the insulative layer at each position corresponding to anelectrode in the second group of electrodes, thereby electricallyconnecting the second row electrical interconnect to electrodes in thesecond group in series (step 3602 d). The insulative layer may beapplied by any suitable means, such as by flowing or spraying theinsulative material onto the partially assembled CESD after firstconnecting the first electrical interconnect to the first group ofelectrodes. In some embodiments, the insulative layer ispoly(p-xylylene). Vias are formed through the insulative layer aboveelectrodes of the second group, and the second electrical interconnectis applied such that the vias connect the second electrical interconnectto the electrodes of the second group. In the exemplary embodiments ofFIGS. 7, 8, and 10-14, the row electrical interconnects 115 are abovethe insulative layer 190, and the column electrical interconnects 125are below the insulative layer 190.

In a unit cell arrangement, there may be multiple planes of electricalinterconnects and multiple insulative layers. For example, the unitcells illustrated in FIGS. 16 and 17 include electrical interconnectsdisposed in four planes. In some embodiments, the illustrated unit celland/or unit cell array therefore includes three insulative layers toseparate the four planes of electrical interconnects. Vias would extendthrough one, two, or all three insulative layers as necessary to provideconnections to the appropriate underlying electrodes.

In any or all of the above embodiments, an upper sealing layer may bedeposited atop the CESD. The upper sealing layer may be an insulativelayer such as, for example, polyp-xylylene). The upper sealing layer isdeposited by any suitable means, such as by flowing or spraying thesealing material onto the assembled CESD.

FIG. 37 is a flow diagram illustrating embodiments of method for makinga stacked CESD as illustrated in FIGS. 22A, 22B, 23, 31, and 32. Themethod includes providing a first electrode (step 3701) and forming astacked arrangement of alternating layers of a dielectric material and aconductive material on the first electrode (step 3702). Optionally(e.g., with respect to tubular CESDs as shown in FIGS. 22A, 22B, 23),the first electrode may be provided by forming the first electrode on asubstrate (step 3700). The stacked arrangement is formed by applying alayer of a dielectric material to a surface of the first electrode (step3703), applying a layer of a conductive material onto the layer of thedielectric material (step 3704), and applying another layer of thedielectric material onto the layer of the conductive material (step3705). If more layers are desired (step 3706), then steps 3704 and 3705are repeated. When the desired number of layers has been formed, adecision is made whether to apply an outer nonconductive sealingmaterial (step 3707). If the optional nonconductive sealing material isdesired, it is applied in contact with one or more side edges of thestacked arrangement (e.g., as shown in FIG. 23) (step 3708). A secondelectrode is applied in contact with the outermost layer, which is adielectric material layer, of the stacked arrangement (step 3709). It isto be understood that optional step 3708 can be performed before step3709 as shown or, alternatively, after step 3709. When making a tubularstacked CESD as shown in FIG. 32, the optional outer nonconductivesealing material 3160 may be applied to the outwardly facing surface3120 b of the second electrode 3120, or to all exterior surfaces of theCESD 3100.

Applying layers of the dielectric material and the conductive materialmay be performed by any suitable method. In some embodiments, layers ofthe dielectric material and/or the conductive material are applied byspraying (e.g., with an air brush), vapor-phase deposition, or othermethods known to those skilled in the art of film formation.Alternatively, dielectric material layers may be applied by flowing asolvent-based dielectric, such as a viscous dielectric, onto the firstelectrode or an underlying conductive material layer. In some instancesthe dielectric material is thickened or solidified, e.g., by removingsolvent, such as by evaporation, or by cross-linking polymers in thedielectric material. An optional nonconductive sealing material isapplied by similar methods.

A removable carrier or substrate on which the first electrode has beenformed may be subsequently removed by any suitable method. For example,a removable carrier comprising a water-soluble polymer can be dissolvedand removed with water.

FIG. 38 is a flow diagram illustrating one embodiment of a generalizedmethod for making a stacked CESD as illustrated in FIGS. 24-26. Themethod includes forming an array of n groups of spaced-apart parallelelectrodes in n parallel planes or layers (step 3801). Optionally, thearray of electrodes is formed on a substrate. The array of electrodesmay be formed by any suitable method, e.g., as described above withrespect to the method of FIG. 35. A group of parallel electrodes in alayer may be oriented at right angles to an adjacent group of parallelelectrodes, or the group of parallel electrodes may be rotated 0-90°relative to the adjacent group of parallel electrodes. Advantageously,the electrodes are arranged such that electrode ends will protrude fromtwo or more sides of a completed quadrilateral CESD as discussed withrespect to FIGS. 24-26. When the electrode array has been formed, spacesbetween the electrodes are filled with a dielectric material (step3802). The dielectric material may be disposed in the spaces by anysuitable method, e.g., as described above with respect to the method ofFIG. 35. A decision is made whether to apply a conductive material (step3803). If the optional conductive material is desired, it is applied incontact with two or more side edges of the stacked arrangement (step3804). The optional conductive material may be applied by any suitablemeans, such as by flowing or spraying the conductive material onto theside edges.

FIG. 39 is a flow diagram illustrating an independent embodiment of ageneralized method for making a stacked CESD as illustrated in FIGS.24-26. The method includes forming a layer of dielectric material andelectrodes (step 3901). Optionally, the layer of dielectric material isformed on a substrate. The layer of dielectric material may be formed byany suitable method, e.g., as described above with respect to the methodof FIG. 35. In one embodiment, a plurality of parallel troughs is formedin an upper surface of the t layer of dielectric material (step 3902 a).The troughs may be formed by any suitable method, such as etching, lasercutting, etc. Advantageously, the troughs are formed such that electrodeends can protrude from or be coincident with one or more side edges ofthe dielectric material layer. An electrode is provided or formed ineach of the troughs (step 3903 a). The electrodes may be provided, forexample, as a wire. Alternatively, the electrodes may be formed in thetroughs, e.g., by filling the troughs with conductive carbon. In anotherembodiment, a plurality of parallel electrodes is applied to an uppersurface of the layer of dielectric material (step 3902 b). Theelectrodes can be applied by any suitable method. For example, a liquidform of the electrodes can be “printed” onto the upper surface of thedielectric material as will be understood by a person of ordinary skillin the art. Alternatively, a layer of electrode material can be appliedto the upper layer of the dielectric material, and then excess electrodematerial removed to leave a plurality of parallel electrodes. Asubsequent layer of dielectric material and electrodes is formed atopthe layer of dielectric material and electrodes (step 3904). Theelectrodes of the subsequent layer may be oriented at right angles tothe electrodes the first layer, or the electrodes of the subsequentlayer may be rotated 0-45° relative to the electrodes of the firstlayer. If additional layers are desired (step 3905), step 3904 isrepeated. When the desired number of layers has been formed, a finallayer of dielectric material is formed atop the dielectric material andelectrodes (step 3906). A decision is made whether to apply an outernonconductive sealing material (step 3907). If the optionalnonconductive sealing material is desired, it is applied in contact withtwo or more side edges of the stacked arrangement (step 3908).

V. Methods of Using a CESD

The disclosed CESDs can be used for energy storage, memory storage, or acombination thereof. Embodiments of a method for using a CESD asdisclosed herein include applying a voltage across a capacitive elementdisposed between an electrode of a first group of electrodes and anadjacent electrode of a second group of electrodes, wherein thecapacitive element is a region of the dielectric material locatedbetween the electrode of the first group and the adjacent electrode ofthe second group, thereby charging the capacitive element to a voltageV1. The applied electric field may be from 0.001 V/μm to 1000 V/μm ormore, based on the average thickness of the dielectric material. In oneembodiment, the applied E-field is from 100 V/μm to 1000 V/μm. In anindependent embodiment, the applied E-field is from 0.001 V/μm to 100V/μm. In another independent embodiment, the applied E-field is from 1V/μm to 5 V/μm.

FIG. 40 is a flow diagram showing a generalized method of charging acapacitive element of a CESD. The method includes providing at processblock 4001 a CESD comprising at least one capacitive element defined bya region of a dielectric material between a first electrode of a firstgroup of electrodes and a second electrode of a second group ofelectrodes, the first group of electrodes connected in series to a firstelectrical interconnect and the second group of electrodes connected inseries to a second electrical interconnect. A voltage is applied acrossthe capacitive element by applying a voltage to the first electricalinterconnect, and connecting the second electrical interconnect to Vssfor a period of time (step 4002).

When the CESD comprises an array of aligned or staggered rows ofelectrodes, each row constituting a group of electrodes (e.g., as shownin FIGS. 3-6 and 15), applying the voltage charges the plurality ofcapacitive elements between the adjacent rows of activated electrodes.Such embodiments may be particularly useful as bulk energy storagedevices or devices in which a higher voltage output is desirable.Indeed, in some examples, all rows may be activated to simultaneouslycharge or discharge all capacitive elements within the CESD.

In embodiments where the CESD comprises an array of rows and columns ofelectrodes (e.g., as shown in FIGS. 7-14), wherein each row compriseselectrodes of a first group alternating with electrodes of one or moreother groups, the first electrical interconnect connects each electrodeof the first group in a row in series, a second group of electrodes notconnected by the first electrical interconnect are connected in a columnin series by the second electrical interconnect, and applying thevoltage charges one or more capacitive elements between two adjacentactivated electrodes. Similarly, when the CESD comprises an array ofunit cells (e.g., as shown in FIGS. 16 and 17), applying the voltagecharges one or more capacitive elements between two adjacent activatedelectrodes. In some embodiments, the CESD is a memory device, and eachcapacitive element has a logic state determined by the voltage appliedacross the capacitive element.

In any of the foregoing embodiments, energy may be supplied from theCESD to a load by providing a circuit including the CESD and a loadconnected to the CESD, wherein the capacitive element is charged to thevoltage V1; and applying a reversed polarization electric potentialacross the capacitive element for a discharge period of time, whereinthe reversed polarization electric potential is less than the voltage V1and less than a voltage that would be generated by the capacitiveelement in a high impedance state, thereby supplying power from thecapacitive element to the load. This method may be advantageous when,for example, the CESD has a large geometry, such as an energy collectorand memory cell or a large energy storage cell. This method also may beused to indirectly increase the voltage output of the CESD to the load.

FIG. 41 is a flow diagram showing a generalized method of supplyingenergy from a CESD to a load. The method includes providing at processblock 4101 a circuit including a CESD having at least one capacitiveelement charged to a first voltage level, the capacitive element definedby a region of a dielectric material between a first electrode and asecond electrode; in some embodiments, the dielectric film comprises anelectroentropic dielectric material as disclosed herein. The firstelectrode is connected to a first electrical interconnect, and thesecond electrode is connected to a second electrical interconnect. Thecapacitive element between the first electrode and the second electrodeis charged by applying a voltage across the capacitive element, e.g., byapplying a voltage to the first electrical interconnect and connectingthe second electrical interconnect to Vss. A person of ordinary skill inthe art understands that, alternatively, the voltage could be applied tothe second electrical interconnect, and the first electricalinterconnect could be connected to Vss. A reversed polarization electricpotential is applied across the capacitive element for a dischargeperiod of time, thereby supplying power from the CESD to the load (step4102). A reversed polarization electric potential may be applied acrossthe capacitive element by connecting one of the first electricalinterconnect and the second electrical interconnect to the load, andconnecting the other of the first electrical interconnect and the secondelectrical interconnect to Vss. For example, if the capacitive elementwas charged by applying a voltage to the first electrical interconnectand grounding the second electrical interconnect, a reversedpolarization electrical potential may be applied by connecting thesecond electrical interconnect to the load and grounding the firstelectrical interconnect. In some embodiments, the CESD comprises aplurality of charged capacitive elements, and the method furthercomprises applying reversed polarization electric potentials across theplurality of charged capacitive elements for the discharge period oftime.

FIG. 42 is a flow diagram showing a generalized method of charging acapacitive element of a stacked CESD (e.g., as shown in FIGS. 24-26).The method includes providing at process block 4201 a stacked CESDcomprising at least one capacitive element defined by a region of adielectric material between a first electrode of a first group ofelectrodes and a second electrode of a second group of electrodes, thefirst group of electrodes connected in parallel to a first conductivematerial and the second group of electrodes connected in parallel to asecond conductive material. A voltage is applied across the capacitiveelement by applying a voltage to the first conductive material, andconnecting the second conductive material to Vss for a period of time(step 4202).

FIG. 43 is a flow diagram showing a generalized method of supplyingenergy from a stacked CESD to a load. The method includes providing atprocess block 4301 a circuit including a stacked CESD having at leastone capacitive element charged to a first voltage level, the capacitiveelement defined by a region of a dielectric material between a firstelectrode and a second electrode; in some embodiments, the dielectricmaterial comprises an electroentropic dielectric material as disclosedherein. The first electrode is connected to a first conductive material,and the second electrode is connected to a second conductive material.The capacitive element between the first electrode and the secondelectrode is charged by applying a voltage across the capacitiveelement, e.g., by applying a voltage to the first conductive materialand connecting the second conductive material to Vss. A person ofordinary skill in the art understands that, alternatively, the voltagecould be applied to the second conductive material, and the firstconductive material could be connected to Vss. A reversed polarizationelectric potential is applied across the capacitive element for adischarge period of time, thereby supplying power from the stacked CESDto the load (step 4302). A reversed polarization electric potential maybe applied across the capacitive element by connecting one of the firstconductive material and the second conductive material to the load, andconnecting the other of the first conductive material and the secondconductive material to Vss, e.g., to ground. For example, if thecapacitive element was charged by applying a voltage to the firstconductive material and grounding the second conductive material, areversed polarization electrical potential may be applied by connectingthe second conductive material to the load and grounding the firstconductive material. In some embodiments, the CESD comprises a pluralityof charged capacitive elements, and the method further comprisesapplying reversed polarization electric potentials across the pluralityof charged capacitive elements for the discharge period of time.

The dielectric material has an “intrinsic capacitance” when it is firstmanufactured in an unpolarized state or starting state (e.g., the stateof the dielectric material after manufacture), which can be modified byan applied voltage. Thus, in any or all of the above embodiments, thecapacitive element may have an intrinsic capacitance, and applying thevoltage across the capacitive element modifies the intrinsiccapacitance. In certain embodiments, the intrinsic capacitance of thecapacitive element remains unchanged when the applied voltage isremoved.

In some embodiments, as shown in the flow diagram of FIG. 44, a methodof reading and writing to a memory device includes providing a memorydevice comprising a CESD (step 4401), and writing to the memory deviceby applying a voltage across a capacitive element disposed between anelectrode of a first group of electrodes and an adjacent electrode of asecond group of electrodes, wherein the capacitive element is a regionof the dielectric material located between the electrode of the firstgroup and the adjacent electrode of the second group, thereby chargingthe capacitive element to a voltage V1 (step 4402). A voltage may beapplied across the capacitive element by applying a voltage to a firstelectrical interconnect connecting electrodes of the first group inseries (step 4402 a), and grounding (or connecting to Vss) a secondelectrical interconnect connecting the electrodes of the second group inseries (step 4402 b). The method may further include reading the memorydevice (step 4403). The memory device may be read by connecting one ofthe first electrical interconnect and the second electrical interconnectto a high impedance sensor (step 4403 a), connecting the other of thefirst electrical interconnect and the second electrical interconnect toground/Vss (step 4403 b), and reading the voltage V1 of the capacitiveelement with the high impedance sensor (step 4403 c).

During the writing of a voltage level to a particular capacitiveelement, the impression of the electric field onto the dielectric in theregion that defines the capacitive element induces a change in thepermittivity of the dielectric material. This change in electricalpermittivity is a function of voltage. As a result, the CESD willfunction as a memory storage device even without the necessity ofaccurate voltage levels. If the voltage level of a particular capacitiveelement is allowed to dissipate (this may be a very long time, e.g., >3seconds), the permittivity of the dielectric material can still bedetermined by utilization of a “pulse” of columbic charge. If thecapacitive element was charged to a given level of voltage, even if thecharge at the electrodes on either side of the capacitive element isdrained, the permittivity of the dielectric material in the regiondefining the capacitive element remains at a level that is consistentwith the voltage (E-field) the dielectric would have had if the E-fieldwere still present. For example, if the capacitive element was chargedto 1V, the dielectric material will have a characteristic permittivityconsistent with the applied voltage. If the electrodes on either side ofthe capacitive element are subsequently disconnected and the voltage ofthe capacitive element partially or fully dissipates, the permittivityof the capacitive element will remain substantially unchanged. Thishysteresis characteristic of the dielectric is advantageous to determinethe voltage level change in the capacitive element upon a small pulse ofamperage to a given capacitive element. This columbic pulse will theninduce a small change in the residual voltage that is proportional tothe permittivity of the dielectric, which is directly proportional tothe capacitance of the capacitive element as set forth below.

The general relation between charge Q, capacitance C, and potential Vis:

Q=C×V  Equation 1

The capacitance C is typically considered a constant physical propertyunder most conditions. The capacitance of a specific capacitive elementin the array can be measured by giving it a very small perturbingcharge. In a capacitive element, the application of an electricpotential (or field) can affect the relative permittivity of thedielectric region that defines the capacitive element. Given that thiseffect is largely a function of the voltage (polarization of thedielectric), this property can be used to determine the state of thecapacitive element without a very accurate measurement of the voltage.The perturbing charge should not be enough to effect a capacitancechange in the capacitive element regardless of its state ofpolarization. Given this condition, when there is a change in thecharge, dQ on the electrodes on either side of the capacitive element,this becomes:

Q+dQ=C×V′  Equation 2

where V′ is the new potential across the capacitive element. Bysubtracting Equation 1 from Equation 2, capacitance C can be determinedas a function of the changes in charge and potential.

$\begin{matrix}{{Q + {dQ} - Q} = {{CV}^{\prime} - {CV}}} & {{Equation}\mspace{14mu} 3} \\{{dQ} = {C \times \left( {V^{\prime} - V} \right)}} & {{Equation}\mspace{14mu} 4} \\{\frac{dQ}{dV} = C} & {{Equation}\mspace{14mu} 5}\end{matrix}$

The value of the capacitive element's capacitance C is compared topredetermined values for charged and uncharged states of the capacitiveelement, and the logic state is thus correlated to the capacitancerather than to a voltage appearing at the electrodes on either side ofthe capacitive element.

In the relationship, C=K*e₀*Nd where A is the area of one of theelectrodes in contact with the region of dielectric material definingthe capacitive element, d is the distance between the electrodes, and e₀is the electrical permittivity of a vacuum (8.8542×10⁻¹² F/m), allquantities are constant except for K, relative permittivity. Thus,voltage is related to the change in capacitance of a given capacitiveelement.

The total polarization of the dielectric is dependent upon at leastthree different mechanisms of energy storage (as defined by curvefitting to a charging curve). The fastest mechanisms for energy storage(charging) are affected by the state of polarization of the longest-termenergy storage mechanism. Thus, as the longest-term energy polarizationtakes place, a measurement of the faster mechanisms of polarizationindicate significant changes. Changes in this fast short-termpolarization can be used to determine what the underlying longer-termpolarization may be.

The original polarization level of the capacitive element is determinedby the measurement of the capacitance of the capacitive element. Acalibration curve of the capacitance of a capacitive element to thepolarization is used to calculate the original programmed polarization.Methods to do this calculation can be as simple as a look-up table,analog voltage reference levels, or mathematical calculations in a logicdevice as is well known.

In this way the length of time allowed to elapse between refreshmentcharges to the capacitive element is greatly extended or practicallyeliminated altogether. Advantageously, the quantity of charge that isused to determine capacitance should be as practically small as possiblefor a given noise level of the electronic switching. Methods for themovement of minute charge levels are known to those versed in the art ofanalog electronics. Determination of the original polarization state ofthe dielectric can be significantly altered by the application of toomuch charge for an extended period of time; so, the smallest amount ofcharge applied singly or in multiple applications generally is used. Inthis way the capabilities of the memory device are extended by such anamount to make utilization of the method extend into very long-termstorage of digital data. Applications such as these are termednon-volatile memory and can be thought to be “permanent” memory and datastorage.

A memory device comprising a CESD may be refreshed by (i) charging acapacitive element in the CESD to a voltage V1, wherein the voltage V1discharges, at least in part, due to leakage over time; (ii)subsequently determining a capacitance C of the capacitive element;(iii) determining, based on the capacitance C, the voltage V1; andrecharging the capacitive element to the voltage V1. In someembodiments, capacitance C is correlated to the voltage V1 and thecapacitance C remains substantially unchanged as the voltage V1discharges due to leakage. The capacitive element in the CESD may becharged to the voltage V1 by applying a voltage to a first electricalinterconnect connecting electrodes of the first group in series, andgrounding (or connecting to Vss) a second electrical interconnectconnecting the electrodes of the second group in series. The capacitanceC of the capacitive element may be determined by (i) reading a voltage Vof the capacitive element; (ii) applying a perturbing charge dQ to thecapacitive element, wherein the perturbing charge dQ has a magnitudesufficient to induce a change in the voltage V without inducing a changein the capacitance C; (iii) subsequently reading a voltage V′ of theEESD; and (iv) determining the capacitance C, where C=dQ/(V′−V). Whenactivating two electrodes addresses multiple capacitive elements, alladdressed capacitive elements are read together, and the values areaveraged.

FIG. 45 is a flow diagram illustrating an exemplary method ofdetermining the capacitance of a capacitive element in a memory devicecomprising a CESD as disclosed herein, and refreshing the memory device.In step 4501, a capacitive element of the CESD is initially charged to avoltage V1. After a period of time has elapsed, the capacitance C of thecapacitive element is determined in step 4502. Determining thecapacitance C may include reading the voltage V of the capacitiveelement (step 4502 a), adding a perturbing charge dQ to the capacitiveelement (step 4502 b), reading the subsequent voltage V′ of thecapacitive element (step 4502 c), and calculating the capacitance C ofthe capacitive element according to Equation 5 (step 4502 d). In someembodiments, the perturbing charge dQ has a magnitude approximatelyequal to a magnitude of discharge due to leakage over time. Themagnitude of discharge may be from 0.1-50% of a charge capacity of thecapacitive element, such as from 1-50%, 1-25%, 1-10%, or 1-5% of thecharge capacity. In certain embodiments, the perturbing charge dQ has amagnitude within a range of 1×10⁻¹⁵ coulombs to 1×10⁻² coulombs, such asa magnitude from 1×10⁻¹⁵ coulombs to 1×10⁻⁶ coulombs, from 1×10⁻¹²coulombs to 1×10⁻⁶ coulombs, or from 1×10⁻¹² coulombs to 1×10⁻¹⁰coulombs. At step 4503, the initial voltage V1 of the capacitive elementis determined based on the capacitance C. Determining V1 may be done bycomparing capacitance C to predetermined values corresponding to statesof charge and discharge of the capacitive element. At step 4504, thecapacitive element is recharged to the initial voltage V1. Rechargingthe capacitive element may be performed by selecting a voltage V2sufficient to recharge the capacitive element to the initial voltage V1(step 4504 a) and then writing the selected voltage V2 to the capacitiveelement (step 4504 b).

A memory device may be read by connecting one of the first electricalinterconnect and the second electrical interconnect to a high impedancesensor, connecting the other of the first electrical interconnect andthe second electrical interconnect to Vss, and reading the voltage V1 ofthe capacitive element with the high impedance sensor. FIG. 46 is a flowdiagram illustrating one method of reading a memory device comprising aCESD as disclosed herein. Upon entering RAM operation (step 4601), thememory device is loaded with data (step 4602). The memory device issubsequently powered down (step 4603). At step 4604, the memory deviceis repowered to an active state. The memory device then enters a bootlogic circuit refresh (step 4605). The memory address is set to memory 0(step 4606), and a capacitance memory read/refresh routine is initiated(step 4606). In the memory read/refresh routine, electricalinterconnects are set to address a memory block (i.e., a plurality ofcapacitive elements) or individual memory location (i.e., one or morecapacitive elements surrounding a single activated electrode (step 4607a), and the voltage V of the memory location(s) is read (step 4607 b). Aperturbing charge dQ is added to the memory location (step 4607 c), andthe voltage V′ is read (step 4607 d). The capacitance of the capacitiveelement(s) is calculated according to Equation 5 (step 4607 e). Thecapacitance is compared to a logic level (step 46070. Applying a voltageto a capacitive element modifies the intrinsic capacitance of thedielectric material. Incremental voltages (e.g., voltages in incrementsof 0.25 V) may be used to modify the intrinsic capacitance inincrements, wherein each incremental capacitance corresponds to a logiclevel of the capacitive element. The intrinsic capacitance remainsunchanged when the applied voltage is removed. Thus, the capacitance isindicative of the originally applied voltage. The comparison may beperformed, for example, using a look-up table which relates capacitanceto initial voltage V. A voltage sufficient to restore the capacitiveelement voltage back to the initial value V associated with the logiclevel is selected and written to the capacitive element (step 4607 g).The routine then is incremented to the next memory location (step 4607h). At step 4608, a query asks whether the last memory position has beenfulfilled. If the answer is no, the memory read/refresh routine isrepeated. If the answer is yes, the boot logic circuit refresh is exitedat step 4609. In some embodiments, a capacitive element can be chargedwith incremental voltages to provide eight logic levels and two bits percapacitive element.

Certain representative embodiments are disclosed in the followingnumbered clauses.

1. A capacitive energy storage device (CESD), comprising: an array ofelectrodes with spaces between the electrodes, the array of electrodescomprising n groups of electrodes in a plane, where n is an integergreater than or equal to 2, each electrode having a central axis Acperpendicular to the plane; an electrical interconnect for each group ofelectrodes, each electrical interconnect connecting electrodes of agroup in series; and a dielectric material occupying the spaces betweenthe electrodes and contacting the electrodes, wherein regions of thedielectric material located between adjacent electrodes definecapacitive elements.

2. The CESD of clause 1, wherein the array comprises aligned rows ofelectrodes such that the central axis of each electrode in a row isaligned with the central axis of an electrode in an adjacent row, eachrow constituting a group of electrodes.

3. The CESD of clause 1, wherein the array comprises staggered rows ofelectrodes such that the central axis of each electrode in a row is notaligned with the central axes of electrodes in an adjacent row, each rowconstituting a group of electrodes.

4. The CESD of clause 1, wherein: the array comprises staggered rows ofthe electrodes such that the central axis of each electrode in a row isnot aligned with the central axes of electrodes in an adjacent row; eachrow further comprises a row electrical interconnect connecting a groupof alternating electrodes in the row in series; and groups of staggeredelectrodes not connected by the row electrical interconnect areconnected in columns by column electrical interconnects, the columnelectrical interconnects being offset from the central axes of thestaggered electrodes, wherein there is a vertical spatial separation ateach intersection where a row electrical interconnect crosses a columnelectrical interconnect.

5. The CESD of clause 1, wherein: the array comprises a grid pattern ofrows and columns of electrodes, wherein each row comprises electrodes ofa row group alternating with electrodes of a plurality of column groups;each row group further comprises a row electrical interconnectconnecting each electrode of the row group in series; and each columngroup further comprises a column electrical interconnect connecting eachelectrode of the column group in series, wherein there is a verticalspatial separation at each intersection where a row electricalinterconnect crosses a column electrical interconnect.

6. The CESD of any one of clauses 3-5, further comprising: an insulativelayer disposed between the row electrical interconnects and the columnelectrical interconnects such that the row electrical interconnects areabove the insulative layer and the column electrical interconnects arebelow the insulative layer; and a via defined by the insulative layerfor each electrode of the row group, the via connecting the electrode tothe row electrical interconnect.

7. The CESD of clause 6, wherein the insulative layer comprisespolymerized p-xylylene or a copolymer comprising p-xylylene and aco-monomer.

8. The CESD of clause 4 or clause 5, wherein: the row electricalinterconnect contacts electrodes of the first group at a height h₁ abovea lower surface of each electrode of the first group; and the columnelectrical interconnect contacts electrodes of the second group at aheight h₂ above a lower surface of each electrode of the second groupwhere h₁≠h₂.

9. The CESD of any one of clauses 1-8 wherein each of the row electricalinterconnects and each of the column electrical interconnects has arectangular, circular, or elliptical cross-sectional profile.

10. The CESD of clause 9, wherein each of the row electricalinterconnects and/or the column electrical interconnects comprises anelectrically insulated metal, a carbonized polymer, conductive carbon,or an electrically conductive polymer.

11. A capacitive energy storage device (CESD), comprising a unit cell,the unit cell comprising: a plurality of electrodes at least forming ashape of a polygon with an electrode at each vertex of the polygon, anumber of electrical interconnects equal to a number of electrodes inthe unit cell, each electrical interconnect connected to a singleelectrode in the unit cell, wherein there is a vertical spatialseparation at each intersection of two or more electrical interconnects,and a dielectric material occupying spaces between the electrodes,wherein regions of the dielectric material located between adjacentelectrodes define capacitive elements.

12. The CESD of clause 11, further comprising an electrode at a centerof the polygon.

13. The CESD of clause 11 or clause 12, wherein the polygon is ahexagon.

14. The CESD of any one of clauses 11-13, further comprising: aninsulative layer disposed between intersecting electrical interconnects;and a via defined by the insulative layer to connect an electricalinterconnect above the insulative layer to an electrode below theelectrical interconnect and insulative layer.

15. The CESD of any one of clauses 11-14, further comprising an array ofthe unit cells.

16. The CESD of clause 15, wherein the array comprises rows of the unitcells.

17. The CESD of clause 16, wherein: the polygon is a hexagon; the unitcell further comprises an electrode at a center of the hexagon; and theunit cells are staggered in the rows such that a center of a hexagon isaligned with an edge of a hexagon in each of the adjacent rows.

18. The CESD of any one of clauses 15-17, wherein collinear electrodesof a corresponding position in two or more unit cells are connected inseries through an electrical interconnect.

19. The CESD of any one of clauses 1-18, further comprising a planarnonconductive substrate, wherein: the array of electrodes is disposed onthe substrate, the central axis of each electrode extending generallyperpendicular to the substrate; and the dielectric material is disposedon the substrate and occupies the spaces between the electrodes.

20. The CESD of clause 19, wherein the planar nonconductive substratecomprises a nonconductive polymer.

21. The CESD of any one of clauses 1-20, wherein each capacitive elementhas an intrinsic capacitance, and the intrinsic capacitance is modifiedby a voltage applied between two electrodes adjacent to the capacitiveelement.

22. The CESD of any one of clauses 1-21, wherein each electrode has aright circular cylindrical configuration, an elliptic cylindricalconfiguration, a polygonal cylindrical configuration, a sphericalconfiguration, or a hemispherical configuration.

23. The CESD of clause 22, wherein a central axis-to-central axisspacing between adjacent electrodes is within a range of 5 nm to 5 mm.

24. The CESD of any one of clauses 1-23, wherein each of the electricalconnects comprises an electrically insulated metal, a carbonizedpolymer, conductive carbon, or an electrically conductive polymer.

25. The CESD of clause 24, wherein the electrically insulated metal is ametal coated with a self-assembled monolayer, poly(p-xylylene), or acombination thereof.

26. The CESD of any one of clauses 1-25, wherein: (i) each electrode hasa height along the central axis of from 50 nm to 1200 μm; (ii) eachelectrode in a group of electrodes has substantially the same heightalong the central axis; (iii) each electrode in the array hassubstantially the same height along the central axis; or (iv) anycombination of (i), (ii), and (iii).

27. A capacitive energy storage device (CESD), comprising: two or moreelectrodes disposed in a co-spiral arrangement with spaces between theelectrodes, wherein the two or more electrodes do not intersect oneanother; and a dielectric material occupying the spaces between theelectrodes and in contact with the electrodes.

28. The CESD of clause 27, wherein the electrodes are spaced equidistantfrom one another throughout the spiral arrangement.

29. The CESD of clause 27 or clause 28, wherein the co-spiralarrangement has a circular, elliptical, or polygonal shape.

30. The CESD of any one of clauses 1-29, wherein the electrodes compriseconductive carbon, a conductive organic material, a conductive metal, ora semiconductor.

31. The CESD of any one of clauses 1-30, wherein each electrode isanodized or coated with polyp-xylylene).

32. The CESD of any one of clauses 1-31, further comprising an uppersealing layer.

33. The CESD of clause 32, wherein the upper sealing layer comprisespolyp-xylylene).

34. The CESD of any one of clauses 1-33, wherein the dielectric materialis an electroentropic dielectric material that has a relativepermittivity greater than 3.9.

35. The CESD of clause 34, wherein the electroentropic dielectricmaterial comprises a plurality of polymeric molecules.

36. The CESD of clause 35, wherein the polymeric molecules compriseproteins, poly(p-xylylene) poly(maleic acid), acrylic acid polymers,methacrylic acid polymers, polyethylene glycol, urethane polymers, epoxypolymers, silicone polymers, terpenoid polymers, naturally occurringresin polymers, polyisocyanates, or combinations thereof.

37. The CESD of clause 35, wherein the polymeric molecules arepoly(p-xylylene), zein, poly(maleic acid), shellac, silicone oil, or acombination thereof.

38. The CESD of any one of clauses 34-37, wherein the electroentropicdielectric material further comprises an inorganic salt.

39. The CESD of clause 38, wherein the inorganic salt comprises a groupIIA metal ion, a group IIIA metal ion, or a combination thereof.

40. The CESD of clause 38, wherein the CESD is a component of a memorydevice, a bulk energy storage device, or a combined memory and energystorage device.

41. A method for making a capacitive energy storage device (CESD)according to any one of clauses 1-26 or 30-40, comprising: forming anarray of electrodes at least partially embedded within or in contactwith a dielectric material with spaces between the electrodes, the arrayof electrodes comprising n groups of electrodes arranged in a singleplane, where n is an integer greater than or equal to 2, each electrodehaving a central axis perpendicular to the plane; connecting electrodesof each group in series with an electrical interconnect, thereby formingthe CESD.

42. The method of clause 41, wherein forming the array of electrodes atleast partially embedded in or in contact with the dielectric materialfurther comprises: forming the array of electrodes; and disposing thedielectric material in the spaces between the electrodes.

43. The method of clause 41 or clause 42, wherein forming the array ofelectrodes comprises forming the electrodes on a substrate bynanolithography, microlithography, shadow-mask polymerization, or ascreening process.

44. The method of clause 41, wherein forming the array of electrodes atleast partially embedded or in contact with in the dielectric materialfurther comprises: forming a layer of a dielectric material on asubstrate; and at least partially embedding the electrodes in thedielectric material or placing the electrodes in contact with thedielectric material to form the array of electrodes.

45. The method of clause 43 or clause 44, wherein the substrate is anonconductive substrate.

46. The method of any one of clauses 43-45, wherein the substrate is aremovable carrier layer, the method further comprising removing thesubstrate after forming the array of electrodes at least partiallyembedded in or in contact with the dielectric material.

47. The method of any one of clauses 41-46, wherein connecting theelectrodes within each group in series comprises: connecting a firstgroup of electrodes in series with a first electrical interconnect; andconnecting a second group of electrodes in series with a secondelectrical interconnect, such that there is a vertical spatialseparation at each intersection where the second electrical interconnectcrosses the first electrical interconnect.

48. The method of clause 47, further comprising: disposing an insulativelayer onto the array of electrodes and the first electrical interconnectsuch that the first electrical interconnect is below the insulativelayer; disposing a second electrical interconnect onto the insulativelayer such that the second electrical interconnect is positioned abovethe insulative layer and above the second group of electrodes; andforming a via through the insulative layer at each positioncorresponding to an electrode in the second group of electrodes, therebyelectrically connecting the second row electrical interconnect toelectrodes in the second group in series.

49. The method of any one of clauses 41-48, further comprisingdepositing an upper sealing layer on the CESD.

50. A method for using a capacitive energy storage device (CESD)according to any one of clauses 1-26 or 30-40, comprising: providing aCESD according to any one of clauses 1-26 or 30-40; and applying avoltage across a capacitive element disposed between an electrode of afirst group of electrodes and an adjacent electrode of a second group ofelectrodes, wherein the capacitive element is a region of the dielectricmaterial located between the electrode of the first group and theadjacent electrode of the second group, thereby charging the capacitiveelement to a voltage V1.

51. The method of clause 50, wherein applying a voltage across thecapacitive element comprises: applying a voltage to a first electricalinterconnect connecting electrodes of the first group in series; andconnecting a second electrical interconnect to Vss, the secondelectrical interconnect connecting the electrodes of the second group inseries.

52. The method of clause 50 or clause 51, wherein: the CESD comprises anarray of aligned or staggered rows of electrodes, each row constitutinga group of electrodes, wherein the device comprises a plurality ofcapacitive elements, each capacitive element defined by a region of thedielectric material located between two electrodes in adjacent rows ofelectrodes; and applying the voltage charges the plurality of capacitiveelements between the adjacent rows of electrodes.

53. The method of clause 50 or clause 51, wherein: the CESD comprises anarray of rows and columns of electrodes, wherein each row compriseselectrodes of a first group alternating with electrodes of one or moreother groups; the first electrical interconnect connects each electrodeof the first group in a row in series; a second group of electrodes notconnected by the first electrical interconnect are connected in a columnin series by the second electrical interconnect; and applying thevoltage charges two or more capacitive elements adjacent to oneelectrode of the first group or the second group.

54. The method of any one of clauses 50-53, further comprising supplyingenergy from the CESD to a load by: providing a circuit including theCESD and a load connected to the CESD, wherein the capacitive element ischarged to the voltage V1; and applying a reversed polarization electricpotential across the capacitive element for a discharge period of time,wherein the reversed polarization electric potential is less than thevoltage V1 and less than a voltage that would be generated by thecapacitive element in a high impedance state, thereby supplying powerfrom the capacitive element to the load.

55. The method of clause 54, wherein applying a reversed polarizationelectric potential across the capacitive element comprises: connectingone of the first electrical interconnect and the second electricalinterconnect to the load; and connecting the other of the firstelectrical interconnect and the second electrical interconnect to Vss.

56. The method of any one of clauses 50-53, wherein the CESD is a memorydevice, and the capacitive element has a logic state determined by thevoltage applied across the capacitive element.

57. The method of any one of clauses 50-56, wherein the capacitiveelement has an intrinsic capacitance, and applying the voltage acrossthe capacitive element modifies the intrinsic capacitance.

58. The method of clause 57, wherein the intrinsic capacitance of thecapacitive element remains unchanged when the applied voltage isremoved.

59. A method of using a memory device, comprising: providing a memorydevice comprising a capacitive energy storage device (CESD) according toany one of clauses 1-26 or 30-40; and writing to the memory device byapplying a voltage across a capacitive element disposed between anelectrode of a first group of electrodes and an adjacent electrode of asecond group of electrodes, wherein the capacitive element is a regionof the dielectric material located between the electrode of the firstgroup and the adjacent electrode of the second group, thereby chargingthe capacitive element to a voltage V1.

60. The method of clause 59, wherein applying a voltage across thecapacitive element comprises: applying a voltage to a first electricalinterconnect connecting electrodes of the first group in series; andconnecting a second electrical interconnect to Vss, the secondelectrical interconnect connecting the electrodes of the second group inseries.

61. The method of clause 59 or clause 60, further comprising reading thememory device by: connecting one of the first electrical interconnectand the second electrical interconnect to a high impedance sensor;connecting the other of the first electrical interconnect and the secondelectrical interconnect to Vss; and reading the voltage V1 of thecapacitive element with the high impedance sensor.

62. A method of refreshing a memory device, comprising: providing acapacitive energy storage device (CESD) according to any one of clauses1-26 or 30-40; charging a capacitive element in the CESD to a voltageV1, wherein the voltage V1 discharges, at least in part, due to leakageover time; subsequently determining a capacitance C of the capacitiveelement; determining, based on the capacitance C, the voltage V1; andrecharging the capacitive element to the voltage V1.

63. The method of clause 62, wherein the capacitance C is correlated tothe voltage V1 and the capacitance C remains substantially unchanged asthe voltage V1 discharges due to leakage.

64. The method of clause 62 or clause 63, wherein charging thecapacitive element in the CESD to a voltage V1 comprises: applying avoltage to a first electrical interconnect connecting electrodes of thefirst group in series; and connecting a second electrical interconnectto Vss, the second electrical interconnect connecting the electrodes ofthe second group in series.

65. The method of any one of clauses 62-64, wherein determining thecapacitance C of the capacitive element comprises: reading a voltage Vof the capacitive element; applying a perturbing charge dQ to thecapacitive element, wherein the perturbing charge dQ has a magnitudesufficient to induce a change in the voltage V without inducing a changein the capacitance C; subsequently reading a voltage V′ of the EESD; anddetermining the capacitance C, where C=dQ/(V′−V).

66. The method of any one of clauses 62-65, wherein determining theinitial voltage V1 prior to leakage comprises comparing the capacitanceC of the capacitive element to predetermined capacitance values for thecapacitive element in charged and uncharged states, thereby correlatingthe capacitance C to the voltage V1.

67. The method of any one of clauses 62-66, wherein recharging the CESDto the voltage V1 comprises: selecting a voltage V2 sufficient torecharge the capacitive element to the voltage V1; and writing theselected voltage V2 to the capacitive element, thereby recharging thecapacitive element to the voltage V1.

68. A method of supplying energy from a capacitive energy storage device(CESD) to a load, comprising: providing a circuit including a CESDaccording to any one of clauses 1-26 or 30-40 and a load connected tothe CESD, the CESD comprising at least one charged capacitive elementthat is charged to a first voltage level, wherein the charged capacitiveelement is disposed between an electrode of a first group of electrodesand an adjacent electrode of a second group of electrodes; and applyinga reversed polarization electric potential across the charged capacitiveelement for a discharge period of time, wherein the reversedpolarization electric potential is less than the first voltage level andless than a voltage that would be generated by the charged capacitiveelement in a high impedance state, thereby supplying power from thecharged capacitive element to the load.

69. The method of clause 68, wherein applying a reversed polarizationelectric potential across the capacitive element comprises: connecting afirst electrical interconnect connecting electrodes of the first groupin series to the load; and connecting a second electrical interconnectconnecting electrodes of the second group in series to Vss.

70. The method of clause 68 or clause 69, wherein the CESD comprises aplurality of charged capacitive elements, the method further comprisingapplying reversed polarization electric potentials across the pluralityof charged capacitive elements for the discharge period of time.

71. A stacked capacitive energy storage device (CESD), comprising: afirst electrode; a second electrode parallel to and spaced apart fromthe first electrode, thereby forming a space between the first andsecond electrodes; and a stacked arrangement of alternating layers of adielectric material and a conductive material disposed parallel to thefirst and second electrodes and occupying the space between the firstand second electrodes, wherein the stacked arrangement comprises xlayers of a dielectric material, wherein (i) x is an integer greaterthan or equal to two, (ii) a first layer of the dielectric material isin direct contact with the first electrode, and (iii) layer x of thedielectric material is in direct contact with the second electrode; andy layers of a conductive material, wherein y=x−1 and a layer of theconductive material is positioned between each pair of adjacent layersof the dielectric material.

72. The stacked CESD of clause 71, wherein the dielectric material is afluid having a viscosity greater than or equal to 0.5 cP.

73. The stacked CESD of clause 71 or clause 72, wherein the dielectricmaterial is an electroentropic dielectric material that has a relativepermittivity greater than 3.9.

74. The stacked CESD of clause 73, wherein the electroentropicdielectric material comprises a plurality of polymeric molecules.

75. The stacked CESD of clause 74, wherein the polymeric moleculescomprise proteins, polyp-xylylene) poly(maleic acid), acrylic acidpolymers, methacrylic acid polymers, polyethylene glycol, urethanepolymers, epoxy polymers, silicone polymers, terpenoid polymers,naturally occurring resin polymers, polyisocyanates, or combinationsthereof.

76. The stacked CESD of clause 75, wherein the polymeric molecules arepolyp-xylylene), zein, poly(maleic acid), shellac, silicone oil, or acombination thereof.

77. The stacked CESD of any one of clauses 71-76, wherein the conductivematerial comprises a carbonaceous material, a metal, a conductivepolymer, or a combination thereof.

78. The stacked CESD of clause 77, wherein the conductive materialcomprises carbon powder, graphene, graphite, aluminum, polyaniline, orpoly(N-methyl pyrrole).

79. The stacked CESD of any one of clauses 71-78, wherein each layer ofthe dielectric material has a thickness within a range of from 0.0001 μmto 100 μm.

80. The stacked CESD of clause 79, wherein the thickness of each layerof the dielectric material is the same.

81. The stacked CESD of any one of clauses 71-80, wherein each layer ofthe conductive material has a thickness within a range of from 0.0005 μmto 10000 μm.

82. The stacked CESD of clause 81, wherein the thickness of each layerof the conductive material is the same.

83. The stacked CESD of any one of clauses 71-82, further comprising anonconductive sealing material in contact with one or more side edges ofthe stacked arrangement and extending from the first electrode to thesecond electrode.

84. The stacked CESD of clause 83, wherein the nonconductive sealingmaterial comprises polymerized p-xylylene, a copolymer comprisingp-xylylene and a co-monomer, or polyethylene terephthalate.

85. The stacked CESD of any one of clauses 71-84, wherein x is aninteger from 2 to 10, and the stacked CESD has a height, as measuredfrom an outwardly facing surface of the first electrode to an outwardlyfacing surface of the second electrode, within a range of from 10 μm to2000 μm.

86. The stacked CESD of any one of clauses 71-84, wherein: the firstelectrode has a cylindrical configuration, an inwardly facing surface,an outwardly facing surface, and an outer diameter; the second electrodehas a cylindrical configuration, an inwardly facing surface, anoutwardly facing surface, and an inner diameter that is greater than theouter diameter of the first electrode; and the stacked arrangement isdisposed between the outwardly facing surface of the first electrode andthe inwardly facing surface of the second electrode in concentricalternating layers of the dielectric material and the conductivematerial.

87. The stacked CESD of clause 86, further comprising an outernonconductive coating in contact with the outwardly facing surface ofthe second electrode.

88. A method for making a stacked capacitive energy storage device(CESD), the method comprising: (a) providing a first electrode; (b)forming a stacked arrangement of alternating layers of a dielectricmaterial and a conductive material by (i) applying a layer of adielectric material to a surface of the first electrode, (ii) applying alayer of a conductive material onto the layer of the dielectricmaterial, and (iii) applying a subsequent layer of the dielectricmaterial onto the layer of the conductive material; and (c) applying asecond electrode in contact with an outermost layer of the stackedarrangement.

89. The method of clause 88, further comprising sequentially repeatingsteps (ii) and (iii) to provide additional alternating layers of thedielectric material and the conductive material, the additionalalternating layers terminating with a layer of the dielectric materialsuch that the stacked arrangement includes x layers of the dielectricmaterial alternating with y layers of the conductive material, wherein xis an integer greater than or equal to 2 and y=x−1.

90. The method of clause 88 or clause 89, further comprising applying anonconductive sealing material in contact with one or more side edges ofthe stacked arrangement and extending from the first electrode to thesecond electrode.

91. A capacitive energy storage device (CESD), comprising: a firstelectrode; a second electrode wrapped in a spiral configuration aroundthe first electrode, wherein there is a space between the firstelectrode and the second electrode; and a dielectric material occupyingthe space between the first electrode and the second electrode and incontact with the first electrode and the second electrode, whereinregions of the dielectric material located between the electrodes definecapacitive elements.

92. The CESD of clause 91, further comprising a third electrode having atubular configuration surrounding the first and second electrodes,wherein there is a space between the third tubular electrode and thesecond electrode, the space filled with the dielectric material.

93. A stacked capacitive energy storage device (CESD), comprising: anarray of electrodes with spaces between the electrodes, the array ofelectrodes comprising n groups of spaced-apart parallel electrodesforming n stacked parallel layers of parallel electrodes where n is aninteger greater than or equal to 2, each electrode having a central axisparallel to the layer; and a dielectric material occupying spacesbetween the electrodes and contacting the electrodes, wherein regions ofthe dielectric material located between adjacent electrodes definecapacitive elements.

92. The stacked CESD of clause 91, wherein the parallel electrodes ineach layer are rotated from 0-90° relative to the parallel electrodes ineach adjacent layer.

93. The stacked CESD of clause 92, wherein the parallel electrodes ineach layer are rotated 90° relative to the parallel electrodes in eachadjacent layer.

94. The stacked CESD of any one of clauses 91-93, wherein the stackedCESD has a quadrilateral configuration defining four side edges and eachelectrode has an end protruding from one side edge of the CESD, thestacked CESD further comprising a conductive material applied to two ormore side edges of the stacked CESD and in contact with the ends ofelectrodes protruding from the side edges to which the conductivematerial is applied.

95. The stacked CESD of any one of clauses 91-94, wherein the electrodescomprise wires having sinuous curves or wires including periodicprotrusions along a length of the wire.

96. The stacked CESD of clause 95, wherein: adjacent electrodes in alayer are oriented such that the sinuous curves or periodic protrusionsof the adjacent electrodes are in phase with one another; or adjacentelectrodes in a layer are oriented such that the sinuous curves orperiodic protrusions of the adjacent electrodes are 180° out of phasewith one another.

97. The CESD of any one of clauses 91-96, wherein each capacitiveelement has an intrinsic capacitance, and the intrinsic capacitance ismodified by a voltage applied between two electrodes adjacent to thecapacitive element.

98. The CESD of any one of clauses 91-97, wherein each electrode has aright circular cylindrical configuration, an elliptic cylindricalconfiguration, a polygonal cylindrical configuration, a sphericalconfiguration, or a hemispherical configuration.

99. The CESD of clause 98, wherein a central axis-to-central axisspacing between adjacent electrodes is within a range of 5 nm to 5 mm.

100. The CESD of any one of clauses 91-99, wherein the electrodescomprise conductive carbon, a conductive organic material, a conductivemetal, or a semiconductor.

101. The CESD of any one of clauses 91-100, wherein each electrode isanodized or coated with poly(p-xylylene).

102. The CESD of any one of clauses 91-101, wherein the dielectricmaterial is an electroentropic dielectric material that has a relativepermittivity greater than 3.9.

103. The CESD of clause 102, wherein the electroentropic dielectricmaterial comprises a plurality of polymeric molecules.

104. The CESD of clause 103, wherein the polymeric molecules compriseproteins, poly(p-xylylene) poly(maleic acid), acrylic acid polymers,methacrylic acid polymers, polyethylene glycol, urethane polymers, epoxypolymers, silicone polymers, terpenoid polymers, naturally occurringresin polymers, polyisocyanates, or combinations thereof.

105. The CESD of clause 103, wherein the polymeric molecules arepoly(p-xylylene), zein, poly(maleic acid), shellac, silicone oil, or acombination thereof.

106. The CESD of any one of clauses 102-105, wherein the electroentropicdielectric material further comprises an inorganic salt.

107. The CESD of clause 106, wherein the inorganic salt comprises agroup IIA metal ion, a group IIIA metal ion, or a combination thereof.

108. A method of making a stacked capacitive energy storage device(CESD) according to any one of clauses 91-107, comprising: forming anarray of electrodes embedded within a dielectric material with spacesbetween the electrodes, the array of electrodes comprising n groups ofparallel electrodes arranged in n stacked parallel planes where n is aninteger greater than or equal to 2, each electrode having a central axisparallel to the stacked parallel planes.

109. The method of clause 108, wherein forming the array of electrodesembedded within the dielectric material comprises: forming the array ofelectrodes; and disposing the dielectric material in the spaces betweenthe electrodes.

110. The method of clause 108, wherein forming the array of electrodesembedded within the dielectric material comprises: (a) forming a firstlayer of a dielectric material on a substrate; (b) at least partiallyembedding a first group of electrodes in the dielectric material; (c)forming a subsequent layer of the dielectric material atop the firstlayer; (d) at least partially embedding a subsequent group of electrodesin the subsequent layer; and (e) repeating steps (c) and (d) until nstacked parallel layers are formed.

111. The method of clause 108, wherein forming the array of electrodesembedded within the dielectric material comprises: (a) forming a firstlayer of a dielectric material on a substrate; (b) forming a pluralityof parallel troughs in an upper surface of the first layer of thedielectric material; (c) placing or forming an electrode in each of theparallel troughs in the first layer to form a first group of electrodes;(d) forming a subsequent layer of the dielectric material atop the firstlayer; (e) forming a plurality of parallel troughs in an upper surfaceof the subsequent layer of the dielectric material; (f) placing orforming an electrode in each of the parallel troughs in the subsequentlayer to form a subsequent group of electrodes; (g) repeating steps(d)-(f) until n stacked parallel planes are formed; and (h) forming anupper layer of dielectric material atop the nth parallel plane.

112. The method of any one of clauses 107-111, wherein the CESD has aquadrilateral configuration defining four side edges, the method furthercomprising applying a conductive material to at least two adjacent sideedges.

113. A method for using a stacked capacitive energy storage device(CESD) according to any one of clauses 91-107, comprising: providing astacked CESD according to any one of clauses 91-107; and applying avoltage across a capacitive element disposed between two adjacentelectrodes, wherein the capacitive element is a region of the dielectricmaterial located between the adjacent electrodes, thereby charging thecapacitive element to a voltage V1.

114. The method of clause 113, wherein providing the stacked CESDcomprises providing a stacked CESD according to clause 94 having a firstconductive material applied to a first side edge of the stacked CESD anda second conductive material applied to an adjacent side edge of thestacked CESD and wherein the two adjacent electrodes are in adjacentlayers of the stacked CESD, the method further comprising: applying avoltage to the first conductive material; and connecting the secondconductive material to Vss.

115. The method of clause 113, wherein providing the stacked CESDcomprises providing a stacked CESD according to clause 94 having a firstconductive material applied to a first side edge of the stacked CESD anda second conductive material applied to an opposing side of the stackedCESD and wherein the two adjacent electrodes are in a single layer ofthe stacked CESD, the method further comprising: applying a voltage tothe first conductive material; and connecting the second conductivematerial to Vss.

116. The method of any one of clauses 113-116, further comprisingsupplying energy from the stacked CESD to a load by: providing a circuitincluding the stacked CESD and a load connected to the stacked CESD,wherein the capacitive element is charged to the voltage V1; andapplying a reversed polarization electric potential across thecapacitive element for a discharge period of time, wherein the reversedpolarization electric potential is less than the voltage V1 and lessthan a voltage that would be generated by the capacitive element in ahigh impedance state, thereby supplying power from the capacitiveelement to the load.

117. The method of clause 116, wherein applying a reversed polarizationelectric potential across the capacitive element comprises: connectingone of the first conductive material and the second conductive materialto the load; and connecting the other of the first conductive materialand the second conductive material to Vss.

In view of the many possible embodiments to which the principles of thedisclosed invention may be applied, it should be recognized that theillustrated embodiments are only preferred examples of the invention andshould not be taken as limiting the scope of the invention. Rather, thescope of the invention is defined by the following claims. We thereforeclaim as our invention all that comes within the scope and spirit ofthese claims.

We claim:
 1. A capacitive energy storage device (CESD), comprising: afirst electrode having a cylindrical configuration; a second electrodewrapped in a spiral configuration around the first electrode, whereinthere is a space between the first electrode and the second electrode;and a dielectric material occupying the space between the firstelectrode and the second electrode and in contact with the firstelectrode and the second electrode, wherein regions of the dielectricmaterial located between the electrodes define capacitive elements. 2.The CESD of claim 1, further comprising a third electrode having atubular configuration surrounding the first and second electrodes,wherein: a space between the third electrode and the second electrode ispresent, the space filled with the dielectric material; and the thirdelectrode has the same polarity as the first electrode and a polarityopposite that of the second electrode during use.
 3. The CESD of claim2, wherein the first, second, and third electrodes each have a centralaxis Ac, where the central axes are coaxial.
 4. The CESD of claim 2,further comprising: a larger spiral electrode wrapped around the thirdelectrode without being in direct contact with the third electrode; alarger tubular electrode surrounding the larger spiral electrode; andadditional dielectric material occupying spaces between the thirdelectrode, larger spiral electrode, and larger tubular electrode.
 5. TheCESD of claim 4, further comprising: a first electrical interconnectconnecting the first electrode, third electrode, and larger tubularelectrode in parallel, the first electrical interconnect comprising anelectrically conductive filament; and a second electrical interconnectconnecting the second electrode and larger spiral electrode in parallel,the second electrical interconnect comprising an electrically conductivefilament.
 6. The CESD of claim 1, wherein the dielectric material has arelative permittivity greater than 3.9.
 7. The CESD of claim 6, whereinthe dielectric material comprises a conductive or nonconductive polymer,an inorganic metal oxide, a mixture of metal oxides, or any combinationthereof.
 8. The CESD of claim 1, further comprising a nonconductivesealing material applied to outer surfaces of the third electrode.
 9. Acapacitive energy storage device (CESD), comprising: a first electrodehaving a cylindrical configuration, an outwardly facing surface, and anouter diameter; a second electrode having a cylindrical configuration,an inwardly facing surface, an outwardly facing surface, and an innerdiameter that is greater than the outer diameter of the first electrode,the second electrode disposed parallel to and spaced apart from thefirst electrode, thereby forming a space between the first and secondelectrodes; and a stacked arrangement of concentric alternating layersof a dielectric material and a conductive material disposed between theoutwardly facing surface of the first electrode and the inwardly facingsurface of the second electrode and occupying the space between thefirst and second electrodes, wherein the stacked arrangement comprises:x layers of a dielectric material, wherein (i) x is an integer greaterthan or equal to two, (ii) a first layer of the dielectric material isin direct contact with the first electrode, and (iii) layer x of thedielectric material is in direct contact with the second electrode; andy layers of a conductive material, wherein y=x−1 and a layer of theconductive material is positioned between each pair of adjacent layersof the dielectric material.
 10. The CESD of claim 9, wherein the firstelectrode is a hollow tube.
 11. The CESD of claim 9, further comprising:an outer nonconductive sealing material in contact with the outwardlyfacing surface of the second electrode; or an outer nonconductivesealing material in contact with all exterior surfaces of the CESD. 12.The CESD of claim 11, wherein the nonconductive sealing materialcomprises polymerized p-xylylene, a copolymer comprising p-xylylene anda co-monomer, polyethylene terephthalate, shellac, polyurethane, orcross-linked polyurethane.
 13. The CESD of claim 9, wherein x is aninteger from 2-5000.
 14. The CESD of claim 9, wherein the first andsecond electrodes independently comprise conductive carbon, a conductiveorganic material other than carbon, a conductive metal, or asemiconductor.
 15. The CESD of claim 9, wherein the conductive materialcomprises a carbonaceous material, a metal, a conductive polymer, or acombination thereof.
 16. The CESD of claim 9, wherein the dielectricmaterial has a relative permittivity greater than 3.9.
 17. The CESD ofclaim 16, wherein the dielectric material comprises a conductive ornonconductive polymer, an inorganic metal oxide, a mixture of metaloxides, or any combination thereof.
 18. A method for making a capacitiveenergy storage device (CESD) according to claim 9, the methodcomprising: (a) providing a first electrode having a cylindricalconfiguration, an outwardly facing surface, and an outer diameter; (b)forming a stacked arrangement of alternating layers of a dielectricmaterial and a conductive material by (i) applying a layer of adielectric material to a surface of the first electrode, (ii) applying alayer of a conductive material onto the layer of the dielectricmaterial, and (iii) applying a subsequent layer of the dielectricmaterial onto the layer of the conductive material; and (c) applying asecond electrode having a cylindrical configuration, an inwardly facingsurface, an outwardly facing surface, and an inner diameter that isgreater than the outer diameter of the first electrode in contact withan outermost layer of the stacked arrangement.
 19. The method of claim18, further comprising sequentially repeating steps (ii) and (iii) toprovide additional alternating layers of the dielectric material and theconductive material, the additional alternating layers terminating witha layer of the dielectric material such that the stacked arrangementincludes x layers of the dielectric material alternating with y layersof the conductive material, wherein x is an integer greater than orequal to 2 and y=x−1.
 20. The method of claim 18, further comprisingapplying a nonconductive sealing material in contact with the outwardlyfacing surface of the second electrode.